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still ensure the security of the system… Is it because skipping that pairing would allow to forge public inputs ? As far I understand, a malicious prover would still have to satisfy all constraints of the quadratic arithmetic program and thus would have to use public inputs satisfying constraints. Or is it because it would be impossible to rework the protocol to have the prover being able to produce proofs that verify ?
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3384:, which depends on the current state of the networking technology and the physical distance between the traders and the exchange, as well as any regulations enforcing a time lag. It then will take time before small-time traders can see the needle having moved. A mathematical model will require too many parameters to be of practical use. --
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only relate A, B, C to one another? I get they're definitions and not merely statements, but I'm not really seeing the difference here. You'd have to define B, C in terms other than A to reach a more meaningful domain. Again, I could look totally foolish right now, since I've never answered a question here before.
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I have been day trading bitcoin for almost a year now. I read articles from bitcoin news to try and guess when the dips and dives will happen and so far it has helped. I just read and article about bitcoin possibly losing freedom to governments and large institutions being able to rig the price. This
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Are you asking about a shorter notation? I may be looking mighty foolish, but isn't it circular and therefore meaningless to write the system of three definitions like you have above? Or rather, wouldn't writing down the first be exactly as meaningful as writing down all three, since both situations
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necessarily distorts the distances, so the scale you get if you take New York and San
Francisco as the two points is generally substantially different from what you get if you take Berlin and Moscow. For maps of the whole Earth it is non-trivial to decide on a "nominal scale". In spite of the name,
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and equatorial scale of 1:20 000 000 for example is 1.18 m high and 1.94 m wide. Out of curiosity, I started to think about dimensions of imaginative humongous world maps. With that as benchmark, if my calculations are correct, a 1:160 000 scale world map, for example, would be 147 m long and 242 m
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If I raise a permutation matrix to a high power it is still a permutation matrix (all values 0 or 1). If I raise a stochastic matrix to a high power it is still a stochastic matrix (all values <=1). But there are a lot of matrices raised to a high power have elements with very large values. Is
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But as a simplification part, why not completely ditch the C parts of the proof when public inputs are used ? That way, the verifier would have to compute 1 pairing in less for verifying the proof. I’m meaning e(C,verifying_key_part). It seems to me the requirement to pair with public inputs would
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The verification algorithm is already simple but I was thinking about some costly environments like blockchains having low block limits. This might be naïve thinking but I was wondering at possibility : normally the prover gives 3 elliptic curves points to the verifier A ; B ; C When public inputs
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You can't define something that already has a meaning. So if A, B and C all have independent meanings, as shown by the use of "denote", then none of them can be defined in terms of the other two. It may be true that A = B + C based on these meanings, but that's not a definition. In any case, you
2978:. This means that there is one way to color 6 circles where all of them are black, 6 where 5 are black and one is red, 15 where 4 are black and 2 are red, 20 where 3 are black and 3 are red, 15 where 2 are black and 4 are red, 6 where one is black and 5 are red, and one where all 6 are red.
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Is it possible for a whale (large bitcoin hodler) to make smaller transactions in a short time to move the price for a larger transaction at a later time? On the upswing this is called 'pump and dump' and 'poop and scoop' on the down swing. Both are illegal in most market trades.
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Just as the seventh row of Pascal's triangle can be used for the classification of ways to make 6 circles all of which are black or red classified by how many are black and how many are red, it is likewise true that the seventh layer of Pascal's tetrahedron can be used for...
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I don't really understand it, no. You're defining A, B, C as the prices of products, but then you're writing abstract definitions of them in terms of each other. Am I missing something? Oh, did you mean to say A is the total? It makes more sense to me that way.
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has happened recently with the German government of Saxony selling off a hoard of seized coin, The Mt. Gox dispersal, and the US dept of
Justice mysteriously moving 30/230k of its seized hoard two days after Trumps bitcoin speech in Nashville raised the price.
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it will use, and then to which part(s) of the projection the scale is to apply (and for some projections, how much of the globe to include). Mapping a spherical surface onto a plane surface cannot be done with a constant scale factor. Eg: you might specify a
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the van der
Grinten projection is not a geometric projection in which points on the map are found by following rays projected along a straight line out of a shrunk globe. The equatorial and central-meridional scales are well defined, though. The length ℓ
2554:, between latitudes +/-85deg, with a scale of 1:10,000,000 at the equator, which would give you a map about 4m wide along the equator, and (judging by the illustration for Mercator) slightly more than that high. Other projections will vary considerably.
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The OP was calling what most people call row 6 "the seventh row" and I thought that was worth pointing out for future reference. Getting caught up in what counts as a "row" and whether statements are parallel is a matter for philosophy and linguistics.
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The spectrum of such a matrix is inside the closed unit disk (a necessary but not sufficient condition). A matrix whose spectrum is in the open unit disk always satisfies this property. I'm not sure there is a general name for this property though.
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By asking whether a new definition can be deduced from an old definition, I mean whether a new claim, that was presented before as an additional definition, can be derived as consequence, from a given assumption that was presened before as an old
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It counts how many ways there are to make 6 circles all of which are black, red, or green, classified by how many are black, how many are red, and how many are green. For example, if you want there to be 2 of each colour, you get
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In any case, I still don't understand what the extra two definitions achieve: either B and C are defined outside of A or they're not, right? If we wanted to know them in terms of A, we already got that in the first definition.
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One way to characterise the set is "a set of vectors, any one of which can be written in terms of the others in a unique way". The set is just A, B and C, i.e. any property of them is a property of the set of them.
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which I would like to deduce, bearing in mind that not all products have a price? Note: Since the latter is a defintion of C, then the existence of A and of B must be derived from the very existence of C.
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where the price moves in microseconds every time a buy/sell happens. Is there a formula for volume needed to move the price in a small time frame or article about time/volume/price/ ratio calculations?
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The reason I posted in math is because I am wondering if a small buy or sell in a quick time frame will actually move the price enough for traders like me who watch the minute candle scale. I use
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I would call 1, 6, 15, ... the sixth row, and the top row, with a single 1, the zeroth row. That's what
Knowledge's does in the articles I've seen at least. Anyway, this should be in the article
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Since my condition requires to be "using A,B,C only, i.e without using S", so I guess you mean the following: "Each vector, can be written as a unique linear combination of the other vectors".
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How can we briefly characterize a given set of vectors, as "linearly dependent - every proper sub set being linearly independent", while we only refer to the vectors rather than to their set?
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If it's intended to be an answer, then please note: My condition requires to be "using A,B,C only, i.e without using S". Additionally, where does your description claim, that S is linearly
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Well, you can call it whatever you want and index it as you like; I'm not going to get into the philosophy of rows. But the formulas are simpler if you start with the top "1" as row 0. --
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After some testing, it seems that rounding suffices at least for r < 100, possibly more. To simplify it, applying Newton's method twice, we can get this approximation which maximizes
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But how about finding the number of ways to make a group of 6 circles, all black or red, classified by how many are black or red. To find out how many ways there are to make a total of
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the powers of the matrix tend to the null matrix, which is not very exciting. I also vaguely remember seeing a theorem that states or implies that when the spectral radius is equal to
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You also have to add that the set {A,B,C} is linearly dependent, but then the description - both uses sets, and also becomes longer than the original one indicated in the title.
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There is another issue in which the definedness of a defined term depends on the definedness of another term, namely when defining a function. Suppose we define a new function
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If A denotes the total price, B denotes the price of the first product, and C denotes the price of the second product, does your definition let us deduce the other definition:
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Using A,B,C only, i.e without using S, what's the shortest description, claiming that the set S is linearly dependent but every proper sub set of S is linearly independent?
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such as the optimal ate pairing e(A,B)=y, then is it possible to fully determine 2 point I and J such as e(I,J) equals a target multiple of the finite’s field element y ?
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It seems the bit about "deducing a definition" articulates a fundamental confusion you have about what you're trying to accomplish. Definitions are stated, not deduced.
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C exist then A exists. Check: A denotes the total price, B denotes the price of the first product, and C denotes the price of the second product: if only the price
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ways to make a group of 6 circles, all black or red, classified by whether each circle is black or red. An example is black-red-black-red-black-red.
2029:. I hope my new question explains also my old question, but if my old question is still not clear, you can ignore it, and focus on my new question.
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are defined. This is more a matter of common sense than anything else, and I see no need for some notational device to express this dependency. --
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You gave the example of prices, so that's what I picked the positive reals* based on. Clearly, you can replace the set with whatever you want.
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2652:. If these scale factors are chosen to be equal, the map will have a height of half its width. For a circular map as shown in the article,
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If A denotes the total price, B denotes the price of the first product, and C denotes the price of the second product, does the definition
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Or does it requires full pairing or full generalized Miller’s inversion and thus would be impossible in practice on a curve like bn254 ?
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The question is, whether we can deduce the latter from the former, i.e. whether we can deduce the new claim from the given assumption.
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of a map is the ratio between the distance between two points on the map and that between the corresponding points on the ground. Any
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Not to bug you, but only since I'm relatively unsure of myself in this area—was this answer something like what you were looking for?
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Sorry for being slow on the uptake. I'm not sure if this needs to fit into any particular system or paradigm: anything wrong with
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is special in that it is operand-wise strictly monotonic and therefore has, at least in the integers and reals (but not in the
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If the values we assign to B and C are logically independent from one another, then no. That's what logical independence means.
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can't deduce a definition. If A has no independent meaning then you can define it to be anything, B + C, B - C, or B * C. --
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You limit the set of the Bs and the Cs to be the positive integers, but my question is general, without limiting anything.
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Please be as specific as possible, and include all relevant context – the usefulness of answers may depend on the context.
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Select the section of the desk that best fits the general topic of your question (see the navigation column to the right).
5319:. I thought analytically I was heading into a dead end. Guess solving it iteratively is still the best for small values.
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To make the tree as dense as possible, I wish to maximise the number of leaf nodes. In other words, how can I find max(
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notation, to make sure that if any value of the above three values A,B,C exists then - all of them exist - and satisfy
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diagrams had me wondering for a given SVG file size, I could add more branches or more depth. Below are two examples:
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3224:, does that statement parallel the statement that trigonometry is simpler if you use radians as opposed to degrees??
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We don't conduct original research or provide a free source of ideas, but we'll help you find information you need.
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How can I calculate the height and width in meters of a future geographic map of the world based on its desired
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Given the optimal ate pairing e(A,B)=y is to possible to determine I and J such as e(I,J)=2y or even e(I,J)=3y?
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There is a unique linear combination generating 0, and in this linear combination all coefficients are nonzero.
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How about a similar application for Pascal's tetrahedron?? Here is the seventh layer of the tetrahedron:
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3. For concluding, that if any value of the above three values A,B,C exists then all of them exist, it's
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Your description, both uses sets, and also becomes longer than the original one indicated in the title.
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4056:. While this is sort of a closed-form expression, it's still unfortunately annoying to work with since
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Post your question to only one section, providing a short header that gives the topic of your question.
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Well, I'm presenting an analogous question (taken from a discipline very close to arithmetic), in my
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using existing known functions with a limited domain. For example, we may define real-valued function
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there a name for the property of a matrix that when raised to a high power remain reasonably valued?
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characters) at the end – this signs and dates your contribution so we know who wrote what and when.
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4205:. The proof of this is annoying so I've put it below, but ultimately what it implies is that when
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https://www.weforum.org/agenda/2024/08/explainer-carry-trades-and-how-they-impact-global-markets/
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Don't post personal contact information – it will be removed. Any answers will be provided here.
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and links to sources. Do not edit others' comments and do not give any medical or legal advice.
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This post may fit better in
Humanities where finance is listed or IT where crypto may belong.
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I return to my initial question then, are you just looking for a shorter notation for this?
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is the main cause of up-spikes since I have been investing and most are followed by dives.
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We don't answer (and may remove) questions that require medical diagnosis or legal advice.
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of the equator is approximately 40,000 km. If the equatorial scale is chosen to be 1 :
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5924:{\displaystyle x=round\left({\frac {9+5.197225r}{2.373852+4.197225\ln(9+r)}}\right)}
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You can say, "each of the sets {A,B}, {A,C} and {B,C} is linearly independent". --
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I realise I can use calculus but I'm unsure what equation I should differentiate.
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Unfortunately, this is actually quite complicated. We can rewrite the problem as
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of a meridian, measured from one pole to the other, is about 40,000 km. Letting
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is a combination of the latency of the connection between the computers of the
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stand for the central-meridional scale factor, the height of the map will be ℓ
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In our case, the given assumption, was presented before as an old definition:
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We don't do your homework for you, though we'll help you past the stuck point.
1140:. Sorry if that hurts anyone to see, haven't flexed these muscles in a while
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3143:{\displaystyle {6 \choose 2,2,2}={6 \choose 2}{4 \choose 2}{2 \choose 2}=90}
3347:, all help to explain how it is possible for whales to control the price.
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https://mpost.io/u-s-unloads-2-billion-in-bitcoin-from-silk-road-seizure/
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the growth of the entries is polynomial in the value of the exponent. --
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The carry trade crash the 1st week of August caused another huge dive.
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Note: A=B+C, and B=A-C, and C=A-B, so the set S is linearly dependent.
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The best answers address the question directly, and back up facts with
5608:{\displaystyle \lceil ({\sqrt {8r-7}}-1)/2\rceil \approx {\sqrt {2r}}}
1689:{\displaystyle B~{\overset {\underset {\mathrm {def} }{}}{=}}~\cdots }
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of the first product exists, we still can't conclude - that the price
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I'm pretty sure that this isn't a math question. But the article on
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Yes, and by symbolic notation the description even becomes shorter.
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having a very large trace, and that I have a pairing with points A∈
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1337:. The new claim, was presened before as an additional definition:
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1990:{\displaystyle C{\overset {\underset {\mathrm {def} }{}}{=}}A-B?}
1384:{\displaystyle C{\overset {\underset {\mathrm {def} }{}}{=}}A-B.}
897:{\displaystyle A{\overset {\underset {\mathrm {def} }{}}{=}}B+C?}
826:{\displaystyle C{\overset {\underset {\mathrm {def} }{}}{=}}A-B.}
771:{\displaystyle B{\overset {\underset {\mathrm {def} }{}}{=}}A-C.}
716:{\displaystyle A{\overset {\underset {\mathrm {def} }{}}{=}}B+C.}
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only makes sense if all terms in the right-hand side are defined
1273:{\displaystyle C{\overset {\underset {\mathrm {def} }{}}{=}}A-B}
584:{\displaystyle A{\overset {\underset {\mathrm {def} }{}}{=}}B+C}
533:{\displaystyle A{\overset {\underset {\mathrm {def} }{}}{=}}B+C}
1133:{\displaystyle \forall (B,C)\in \mathbb {R} ^{+},\exists A=B+C}
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changes do not only always increase but may even decrease. --
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Yep. I've just made it clear in 4# (thanks to your question).
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We don't answer requests for opinions, predictions or debate.
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4234:, as far as I can tell, the best you can do is either round
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linearly independent elements' (in the give example k=2). --
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3986:. Inverting it is complicated, but Wolfram Alpha gives us
5250:), two iterations will bring you close enough; then test
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Is your response a suggestion of rephrasing my question?
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of the second product exists - nor that the total price
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ways, which is exactly the middle entry of this layer.
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For a map of the world, you will have to specify which
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make senee? If it does, can you deduce the definition:
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to be defined by this equation for some given value of
846:(to write down all three defintions), but is there any
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I've just added an addition to 2#, to make it clear.
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is not defined. It just does not make sense. And if
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is not only irrational, but transcendental as well.
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5693:
5653:
5607:
5535:
5493:
5473:
5294:
5268:
5242:
5210:
5143:
5108:
5079:
5059:
4989:
4949:
4899:
4871:
4849:
4821:
4788:
4762:
4739:
4712:
4686:
4639:
4613:
4571:
4539:
4489:
4437:
4399:
4343:
4317:
4266:
4246:
4224:
4197:
4171:
4125:
4068:
4044:
4024:
3978:
3958:
3938:
3891:
3871:
3810:
3763:
3730:
3710:
3690:
3612:
3592:
3142:
2970:
2914:
2896:, you use the n+1th row of Pascal's triangle. For
2880:
2857:
2824:
2797:
2747:
2720:
2413:
2360:
2340:
2311:
2265:
2245:
2060:For example: S is a set of the following vectors:
1989:
1913:
1883:
1853:
1830:
1797:
1731:
1711:
1688:
1639:
1619:
1599:
1579:
1556:
1515:
1492:
1468:
1383:
1272:
1132:
896:
825:
770:
715:
643:
623:
603:
583:
532:
481:
461:
441:
369:
346:
3128:
3115:
3106:
3093:
3084:
3071:
3059:
3032:
2246:{\displaystyle v_{1},v_{2},\dots ,v_{k}\in R^{n}}
1798:{\displaystyle f(x)={\sqrt {1-x}}+{\sqrt {1+x}}.}
1456:This is totally confused. The addition operation
4274:and compare values to get the max over integers.
3565:
4126:{\displaystyle W(z)=w\Leftrightarrow z=we^{w}}
3423:Or even maybe both of the assumptions above ?
2922:, this means we use the seventh row, which is
2805:circles all black or red, the formula is just
5211:{\displaystyle x^{*}={\frac {x+r}{2+\ln x}}.}
2782:The following is a use of Pascal's triangle:
8:
5589:
5550:
5289:
5283:
5263:
5257:
4944:
4938:
4394:
4388:
3307:does explicitly mention cryptocurrencies. --
631:of the first product exists - and the price
5334:P.S. It seems there's an interesting trend:
2630:this comes out as about 250 m. The length ℓ
1567:. It is not just that this fails to define
5461:Unfortunately, serendipity. The number of
4280:
4254:for convenience, or take floor/ceiling of
2522:Converting map scale into height and width
410:1. Since the expression in the title is a
5867:
5840:
5806:
5785:
5779:
5708:
5706:
5671:
5666:
5631:
5620:
5595:
5581:
5556:
5548:
5510:
5486:
5466:
5446:–1th triangular number + 2. Serendipity?
5281:
5255:
5229:
5173:
5164:
5158:
5135:
5123:
5095:
5072:
5031:
4967:
4962:
4929:
4925:
4924:
4915:
4889:
4884:
4864:
4839:
4834:
4807:
4801:
4775:
4755:
4731:
4725:
4705:
4672:
4657:
4652:
4626:
4605:
4587:
4552:
4502:
4452:
4412:
4379:
4375:
4374:
4365:
4330:
4295:
4290:
4259:
4239:
4211:
4184:
4149:
4138:
4117:
4081:
4061:
4037:
4002:
3991:
3971:
3951:
3904:
3884:
3861:
3823:
3776:
3749:
3743:
3723:
3703:
3640:
3625:
3605:
3575:
3563:
3127:
3114:
3112:
3105:
3092:
3090:
3083:
3070:
3068:
3058:
3031:
3029:
3027:
2927:
2901:
2873:
2843:
2837:
2816:
2810:
2790:
2739:
2733:
2712:
2706:
2376:
2353:
2327:
2303:
2284:
2278:
2258:
2237:
2224:
2205:
2192:
2186:
1961:
1953:
1948:
1898:
1896:
1868:
1866:
1843:
1814:
1779:
1763:
1746:
1724:
1704:
1667:
1659:
1652:
1632:
1612:
1592:
1572:
1528:
1508:
1485:
1461:
1355:
1347:
1342:
1247:
1239:
1234:
1103:
1099:
1098:
1074:
868:
860:
855:
797:
789:
784:
742:
734:
729:
687:
679:
674:
636:
616:
596:
558:
550:
545:
507:
499:
494:
474:
454:
434:
359:
336:
4179:is irrational for all positive rational
3691:{\displaystyle \ln(x^{r-x})=(r-x)\ln(x)}
3372:The time needed to move the needle with
3193:, is the top row "1" not really a row??
425:2. However, we can't conclude that if B
4283:
3416:are used C/the inputs vector is split.
2888:circles all black or red classified by
2149:2A04:4A43:900F:F4C3:49F4:4EFB:C442:608F
1647:is not defined, writing something like
611:exists if and only if both - the price
4879:must be irrational and is nonzero, so
4540:{\displaystyle W(er)=1\Rightarrow r=1}
4490:{\displaystyle W(er)=0\Rightarrow r=0}
3620:instead of just integers. Notice that
3360:2604:3D08:5E7A:6A00:D94:3638:168B:18A0
3287:2604:3D08:5E7A:6A00:D94:3638:168B:18A0
5302:to get the optimal integer value. --
2697:Simple question : let’s say I have a
2371:each of the columns of the matrix of
7:
4857:is rational, which is contradictory.
4325:is irrational for positive rational
3425:2A01:E0A:401:A7C0:9CB:33F3:E8EB:8A5D
2760:2A01:E0A:401:A7C0:9CB:33F3:E8EB:8A5D
2483:2404:2000:2000:8:FDE8:8311:95E3:654D
1739:on the real numbers by the equation
540:only tells us (besides the relation
5969:Knowledge resources for researchers
3357:Foreign_exchange_market#Carry_trade
1500:. In general, this is not possible.
227:Knowledge:Reference desk/Guidelines
159:How can I get my question answered?
5701:, which in turn grows faster than
3119:
3097:
3075:
3036:
2312:{\displaystyle v_{1},\dots ,v_{k}}
1968:
1965:
1962:
1674:
1671:
1668:
1362:
1359:
1356:
1254:
1251:
1248:
1112:
1076:
875:
872:
869:
804:
801:
798:
749:
746:
743:
694:
691:
688:
565:
562:
559:
514:
511:
508:
43:Welcome to the mathematics section
31:
5753:, these first differences in the
5269:{\displaystyle \lfloor x\rfloor }
3168:, and can be further extended to
2421:minors of V has a non-zero entry.
2414:{\displaystyle (k-1)\times (k-1)}
2319:. The stated condition is then:
244:
55:
2971:{\displaystyle 1,6,15,20,15,6,1}
45:of the Knowledge reference desk.
34:
5295:{\displaystyle \lceil x\rceil }
3872:{\displaystyle -\ln(x)+(r-x)/x}
651:of the second product exists.
5911:
5899:
5688:
5682:
5648:
5639:
5578:
5553:
5457:17:06, 30 September 2024 (UTC)
5330:11:45, 30 September 2024 (UTC)
5307:10:17, 30 September 2024 (UTC)
5018:02:41, 30 September 2024 (UTC)
4984:
4975:
4525:
4516:
4507:
4475:
4466:
4457:
4432:
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4303:
4166:
4157:
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4092:
4086:
4019:
4010:
3933:
3927:
3858:
3846:
3840:
3834:
3805:
3799:
3790:
3778:
3685:
3679:
3670:
3658:
3652:
3633:
3587:
3568:
3553:00:50, 30 September 2024 (UTC)
3433:11:51, 29 September 2024 (UTC)
3408:verifier‑side simplification ?
3389:08:51, 29 September 2024 (UTC)
3368:17:48, 28 September 2024 (UTC)
3317:13:22, 28 September 2024 (UTC)
3295:08:38, 28 September 2024 (UTC)
3249:02:20, 28 September 2024 (UTC)
3234:01:04, 28 September 2024 (UTC)
3217:00:55, 28 September 2024 (UTC)
3203:21:02, 27 September 2024 (UTC)
3186:17:25, 27 September 2024 (UTC)
3160:14:55, 27 September 2024 (UTC)
3016:14:06, 27 September 2024 (UTC)
2768:15:51, 26 September 2024 (UTC)
2673:10:14, 24 September 2024 (UTC)
2585:20:35, 23 September 2024 (UTC)
2566:18:07, 23 September 2024 (UTC)
2540:15:35, 23 September 2024 (UTC)
2509:08:42, 23 September 2024 (UTC)
2491:00:00, 23 September 2024 (UTC)
2475:08:40, 23 September 2024 (UTC)
2461:21:05, 22 September 2024 (UTC)
2450:08:41, 23 September 2024 (UTC)
2436:17:36, 22 September 2024 (UTC)
2408:
2396:
2390:
2378:
2175:15:52, 22 September 2024 (UTC)
2157:15:15, 22 September 2024 (UTC)
2140:14:56, 22 September 2024 (UTC)
2119:14:46, 22 September 2024 (UTC)
2093:13:30, 22 September 2024 (UTC)
2039:13:38, 22 September 2024 (UTC)
2021:05:29, 22 September 2024 (UTC)
2006:02:13, 22 September 2024 (UTC)
1926:22:29, 20 September 2024 (UTC)
1825:
1819:
1757:
1751:
1551:
1539:
1426:13:17, 22 September 2024 (UTC)
1401:13:08, 22 September 2024 (UTC)
1316:05:34, 22 September 2024 (UTC)
1291:02:21, 22 September 2024 (UTC)
1225:02:08, 22 September 2024 (UTC)
1200:02:05, 22 September 2024 (UTC)
1186:20:10, 20 September 2024 (UTC)
1161:14:31, 20 September 2024 (UTC)
1091:
1079:
1065:13:55, 20 September 2024 (UTC)
1051:13:52, 20 September 2024 (UTC)
1026:13:49, 20 September 2024 (UTC)
1012:13:45, 20 September 2024 (UTC)
986:13:43, 20 September 2024 (UTC)
960:13:40, 20 September 2024 (UTC)
950:It seems you haven't read 2#.
946:13:34, 20 September 2024 (UTC)
919:13:26, 20 September 2024 (UTC)
382:21:55, 20 September 2024 (UTC)
323:02:08, 20 September 2024 (UTC)
305:23:07, 19 September 2024 (UTC)
289:22:12, 19 September 2024 (UTC)
1:
3593:{\displaystyle \max(x^{r-x})}
3349:Fear_of_missing_out#Investing
1914:{\displaystyle {\sqrt {1+x}}}
1884:{\displaystyle {\sqrt {1-x}}}
1696:only increases the confusion.
5721:{\displaystyle {\sqrt {2r}}}
5022:Here is a numerical recipe (
3176:is relevant here as well. --
2778:Uses of Pascal's tetrahedron
5942:04:14, 1 October 2024 (UTC)
5766:03:58, 1 October 2024 (UTC)
5738:03:46, 1 October 2024 (UTC)
4687:{\displaystyle r/w=e^{w-1}}
3939:{\displaystyle r=x+x\ln(x)}
3811:{\displaystyle (r-x)\ln(x)}
2777:
2609:, the width of the map is ℓ
1523:by an equation of the form
219:How do I answer a question?
171:Type '~~~~' (that is, four
48:
5995:
5505:. Although it starts with
5060:{\displaystyle r=x+x\ln x}
4720:is nonzero rational, then
4647:, we can rearrange to get
2572:van der Grinten projection
1861:it is necessary that both
842:: as I've indicated, it's
210:Ready? Ask a new question!
98:
5654:{\displaystyle x=r/W(er)}
5151:until convergence, where
4829:is transcendental, while
4614:{\displaystyle er=we^{w}}
4572:{\displaystyle w\neq 0,1}
4172:{\displaystyle x=r/W(er)}
4076:is implicitly defined as
4025:{\displaystyle x=r/W(er)}
2832:. For example, there are
2341:{\displaystyle k\times k}
2181:Assuming the vectors are
1418:
1308:
1217:
1178:
1153:
1043:
1004:
978:
938:
5979:Knowledge reference desk
5694:{\displaystyle r/\ln(r)}
5118:Iterate the replacement
4770:is rational, then since
4698:Lindemann's 1882 theorem
4438:{\displaystyle w:=W(er)}
3600:, and consider all real
2858:{\displaystyle 2^{6}=64}
1557:{\displaystyle A=f(B,C)}
591:), that the total price
125:Help searching Knowledge
18:Knowledge:Reference desk
5536:{\displaystyle 1,2,3,4}
5243:{\displaystyle r<90}
5144:{\displaystyle x=x^{*}}
4990:{\displaystyle r/W(er)}
4822:{\displaystyle e^{w-1}}
4789:{\displaystyle w\neq 1}
4640:{\displaystyle w\neq 0}
4344:{\displaystyle r\neq 1}
4318:{\displaystyle r/W(er)}
4198:{\displaystyle r\neq 1}
3764:{\displaystyle x^{r-x}}
3536:are positive integers?
1503:Defining some quantity
313:That's it. Thank you!
5925:
5827:
5795:
5742:Note that, unlike for
5722:
5695:
5655:
5609:
5537:
5495:
5475:
5296:
5270:
5244:
5212:
5145:
5110:
5081:
5061:
4991:
4951:
4901:
4873:
4851:
4823:
4790:
4764:
4741:
4714:
4688:
4641:
4615:
4573:
4541:
4491:
4439:
4401:
4345:
4319:
4268:
4248:
4227:
4199:
4173:
4127:
4070:
4046:
4026:
3980:
3960:
3940:
3893:
3873:
3818:is. Its derivative is
3812:
3765:
3732:
3712:
3692:
3614:
3594:
3501:
3491:
3374:high-frequency trading
3144:
2972:
2916:
2882:
2859:
2826:
2799:
2749:
2722:
2699:pairing friendly curve
2415:
2362:
2342:
2313:
2267:
2247:
1991:
1915:
1885:
1855:
1832:
1799:
1733:
1713:
1690:
1641:
1621:
1601:
1581:
1558:
1517:
1494:
1470:
1385:
1274:
1134:
898:
827:
772:
717:
645:
625:
605:
585:
534:
489:exists. The defintion
483:
463:
443:
371:
348:
331:is strictly less than
5974:Knowledge help forums
5926:
5828:
5826:{\displaystyle x+y=r}
5796:
5794:{\displaystyle x^{y}}
5723:
5696:
5656:
5610:
5538:
5496:
5476:
5297:
5271:
5245:
5213:
5146:
5111:
5082:
5062:
4992:
4952:
4902:
4874:
4852:
4824:
4791:
4765:
4742:
4740:{\displaystyle e^{k}}
4715:
4689:
4642:
4616:
4574:
4542:
4492:
4440:
4402:
4346:
4320:
4269:
4249:
4228:
4225:{\displaystyle r: -->
4200:
4174:
4128:
4071:
4047:
4027:
3981:
3961:
3941:
3894:
3874:
3813:
3766:
3733:
3713:
3693:
3615:
3595:
3499:
3489:
3471:are positive integers
3270:Bitcoin price rigging
3172:. The article on the
3145:
2973:
2917:
2883:
2860:
2827:
2825:{\displaystyle 2^{n}}
2800:
2750:
2748:{\displaystyle G_{2}}
2723:
2721:{\displaystyle G_{1}}
2416:
2363:
2343:
2314:
2268:
2248:
1992:
1916:
1886:
1856:
1833:
1800:
1734:
1714:
1691:
1642:
1622:
1602:
1582:
1559:
1518:
1495:
1471:
1386:
1275:
1135:
899:
828:
773:
718:
646:
626:
606:
586:
535:
484:
464:
444:
372:
349:
118:Want a faster answer?
5839:
5805:
5801:for these values of
5778:
5705:
5665:
5619:
5547:
5509:
5485:
5465:
5280:
5254:
5228:
5157:
5122:
5094:
5071:
5030:
4961:
4914:
4883:
4863:
4833:
4800:
4774:
4754:
4724:
4704:
4651:
4625:
4586:
4551:
4501:
4451:
4411:
4364:
4329:
4289:
4258:
4238:
4210:
4183:
4137:
4080:
4060:
4036:
3990:
3970:
3950:
3903:
3883:
3822:
3775:
3742:
3722:
3711:{\displaystyle \ln }
3702:
3624:
3604:
3562:
3490:2 branches, depth 12
3026:
2926:
2900:
2872:
2836:
2809:
2789:
2732:
2705:
2375:
2352:
2326:
2277:
2257:
2185:
2105:I'd just say 'S has
1947:
1895:
1865:
1842:
1831:{\displaystyle f(x)}
1813:
1745:
1723:
1703:
1651:
1631:
1611:
1591:
1571:
1527:
1507:
1484:
1460:
1341:
1233:
1073:
854:
783:
728:
673:
635:
615:
595:
544:
493:
473:
453:
433:
358:
335:
274:Property of a matrix
5418:4⁴, 4⁵, 4⁶ and 4⁷.
5109:{\displaystyle x=9}
4900:{\displaystyle r/w}
4850:{\displaystyle r/w}
3500:4 branches, depth 8
3404:Is this a possible
3174:Multinomial theorem
2915:{\displaystyle n=6}
2552:Mercator projection
327:Note that when the
5921:
5823:
5791:
5757:-values for which
5718:
5691:
5661:grows faster than
5651:
5605:
5533:
5491:
5471:
5292:
5266:
5240:
5208:
5141:
5106:
5077:
5057:
4987:
4947:
4897:
4869:
4847:
4819:
4786:
4760:
4737:
4710:
4684:
4637:
4611:
4569:
4537:
4487:
4435:
4397:
4341:
4315:
4264:
4244:
4222:
4195:
4169:
4123:
4066:
4054:Lambert W function
4042:
4022:
3976:
3956:
3936:
3889:
3869:
3808:
3771:is maximized when
3761:
3728:
3718:is monotonic over
3708:
3688:
3610:
3590:
3502:
3492:
3140:
3003:
3000:
2997:
2994:
2991:
2988:
2985:
2968:
2912:
2890:how many are black
2878:
2855:
2822:
2795:
2745:
2718:
2411:
2358:
2338:
2309:
2273:whose columns are
2263:
2253:, form the matrix
2243:
1987:
1972:
1911:
1881:
1854:{\displaystyle x,}
1851:
1828:
1795:
1729:
1709:
1686:
1678:
1637:
1617:
1597:
1577:
1554:
1513:
1490:
1466:
1381:
1366:
1270:
1258:
1130:
894:
879:
823:
808:
768:
753:
713:
698:
641:
621:
601:
581:
569:
530:
518:
479:
459:
439:
370:{\displaystyle 1,}
367:
347:{\displaystyle 1,}
344:
24:Knowledge:RD/Maths
5915:
5716:
5603:
5570:
5494:{\displaystyle x}
5474:{\displaystyle r}
5422:
5421:
5311:Thanks so much, @
5203:
5080:{\displaystyle x}
5005:
5004:
4910:We conclude that
4872:{\displaystyle w}
4763:{\displaystyle w}
4713:{\displaystyle k}
4267:{\displaystyle x}
4247:{\displaystyle x}
4069:{\displaystyle W}
4045:{\displaystyle W}
3979:{\displaystyle x}
3959:{\displaystyle r}
3892:{\displaystyle 0}
3731:{\displaystyle x}
3613:{\displaystyle x}
3506:
3505:
3380:and those of the
3341:Short and distort
3126:
3104:
3082:
3057:
3002:1 6 15 20 15 6 1
3001:
2998:
2995:
2992:
2989:
2986:
2983:
2881:{\displaystyle n}
2798:{\displaystyle n}
2361:{\displaystyle V}
2266:{\displaystyle V}
1973:
1958:
1909:
1879:
1790:
1774:
1732:{\displaystyle f}
1712:{\displaystyle f}
1682:
1679:
1664:
1658:
1640:{\displaystyle B}
1620:{\displaystyle C}
1600:{\displaystyle B}
1580:{\displaystyle A}
1516:{\displaystyle A}
1493:{\displaystyle -}
1469:{\displaystyle +}
1367:
1352:
1259:
1244:
880:
865:
809:
794:
754:
739:
699:
684:
664:three definitions
644:{\displaystyle C}
624:{\displaystyle B}
604:{\displaystyle A}
570:
555:
519:
504:
482:{\displaystyle A}
462:{\displaystyle C}
442:{\displaystyle B}
418:C exist as well.
53:Select a section:
22:(Redirected from
5986:
5930:
5928:
5927:
5922:
5920:
5916:
5914:
5882:
5868:
5832:
5830:
5829:
5824:
5800:
5798:
5797:
5792:
5790:
5789:
5752:
5727:
5725:
5724:
5719:
5717:
5709:
5700:
5698:
5697:
5692:
5675:
5660:
5658:
5657:
5652:
5635:
5614:
5612:
5611:
5606:
5604:
5596:
5585:
5571:
5557:
5542:
5540:
5539:
5534:
5501:is the sequence
5500:
5498:
5497:
5492:
5480:
5478:
5477:
5472:
5348:
5347:
5301:
5299:
5298:
5293:
5275:
5273:
5272:
5267:
5249:
5247:
5246:
5241:
5217:
5215:
5214:
5209:
5204:
5202:
5185:
5174:
5169:
5168:
5150:
5148:
5147:
5142:
5140:
5139:
5115:
5113:
5112:
5107:
5086:
5084:
5083:
5078:
5067:for real-valued
5066:
5064:
5063:
5058:
4996:
4994:
4993:
4988:
4971:
4956:
4954:
4953:
4948:
4934:
4933:
4928:
4906:
4904:
4903:
4898:
4893:
4878:
4876:
4875:
4870:
4856:
4854:
4853:
4848:
4843:
4828:
4826:
4825:
4820:
4818:
4817:
4795:
4793:
4792:
4787:
4769:
4767:
4766:
4761:
4746:
4744:
4743:
4738:
4736:
4735:
4719:
4717:
4716:
4711:
4700:implies that if
4693:
4691:
4690:
4685:
4683:
4682:
4661:
4646:
4644:
4643:
4638:
4620:
4618:
4617:
4612:
4610:
4609:
4578:
4576:
4575:
4570:
4546:
4544:
4543:
4538:
4496:
4494:
4493:
4488:
4444:
4442:
4441:
4436:
4406:
4404:
4403:
4398:
4384:
4383:
4378:
4350:
4348:
4347:
4342:
4324:
4322:
4321:
4316:
4299:
4281:
4273:
4271:
4270:
4265:
4253:
4251:
4250:
4245:
4233:
4230:
4229:
4223:
4204:
4202:
4201:
4196:
4178:
4176:
4175:
4170:
4153:
4132:
4130:
4129:
4124:
4122:
4121:
4075:
4073:
4072:
4067:
4051:
4049:
4048:
4043:
4031:
4029:
4028:
4023:
4006:
3985:
3983:
3982:
3977:
3965:
3963:
3962:
3957:
3945:
3943:
3942:
3937:
3898:
3896:
3895:
3890:
3878:
3876:
3875:
3870:
3865:
3817:
3815:
3814:
3809:
3770:
3768:
3767:
3762:
3760:
3759:
3737:
3735:
3734:
3729:
3717:
3715:
3714:
3709:
3697:
3695:
3694:
3689:
3651:
3650:
3619:
3617:
3616:
3611:
3599:
3597:
3596:
3591:
3586:
3585:
3482:
3481:
3443:How to find max(
3170:Pascal's simplex
3166:Pascal's pyramid
3149:
3147:
3146:
3141:
3133:
3132:
3131:
3118:
3111:
3110:
3109:
3096:
3089:
3088:
3087:
3074:
3064:
3063:
3062:
3056:
3035:
2999:6 30 60 60 30 6
2977:
2975:
2974:
2969:
2921:
2919:
2918:
2913:
2894:how many are red
2887:
2885:
2884:
2879:
2864:
2862:
2861:
2856:
2848:
2847:
2831:
2829:
2828:
2823:
2821:
2820:
2804:
2802:
2801:
2796:
2754:
2752:
2751:
2746:
2744:
2743:
2727:
2725:
2724:
2719:
2717:
2716:
2667:
2663:
2656:
2648:
2637:
2629:
2624:
2616:
2605:
2570:My own map with
2564:
2420:
2418:
2417:
2412:
2367:
2365:
2364:
2359:
2347:
2345:
2344:
2339:
2318:
2316:
2315:
2310:
2308:
2307:
2289:
2288:
2272:
2270:
2269:
2264:
2252:
2250:
2249:
2244:
2242:
2241:
2229:
2228:
2210:
2209:
2197:
2196:
2104:
2027:following thread
1996:
1994:
1993:
1988:
1974:
1971:
1960:
1954:
1942:
1920:
1918:
1917:
1912:
1910:
1899:
1890:
1888:
1887:
1882:
1880:
1869:
1860:
1858:
1857:
1852:
1837:
1835:
1834:
1829:
1804:
1802:
1801:
1796:
1791:
1780:
1775:
1764:
1738:
1736:
1735:
1730:
1718:
1716:
1715:
1710:
1695:
1693:
1692:
1687:
1681:
1680:
1677:
1666:
1660:
1657:
1646:
1644:
1643:
1638:
1626:
1624:
1623:
1618:
1606:
1604:
1603:
1598:
1586:
1584:
1583:
1578:
1563:
1561:
1560:
1555:
1522:
1520:
1519:
1514:
1499:
1497:
1496:
1491:
1475:
1473:
1472:
1467:
1424:
1422:
1416:
1412:
1390:
1388:
1387:
1382:
1368:
1365:
1354:
1348:
1336:
1314:
1312:
1306:
1302:
1279:
1277:
1276:
1271:
1260:
1257:
1246:
1240:
1223:
1221:
1215:
1211:
1184:
1182:
1176:
1172:
1159:
1157:
1151:
1147:
1139:
1137:
1136:
1131:
1108:
1107:
1102:
1049:
1047:
1041:
1037:
1010:
1008:
1002:
998:
984:
982:
976:
972:
944:
942:
936:
932:
903:
901:
900:
895:
881:
878:
867:
861:
832:
830:
829:
824:
810:
807:
796:
790:
777:
775:
774:
769:
755:
752:
741:
735:
722:
720:
719:
714:
700:
697:
686:
680:
650:
648:
647:
642:
630:
628:
627:
622:
610:
608:
607:
602:
590:
588:
587:
582:
571:
568:
557:
551:
539:
537:
536:
531:
520:
517:
506:
500:
488:
486:
485:
480:
468:
466:
465:
460:
448:
446:
445:
440:
406:
376:
374:
373:
368:
353:
351:
350:
345:
221:
211:
161:
153:
137:
120:
111:
38:
27:
5994:
5993:
5989:
5988:
5987:
5985:
5984:
5983:
5959:
5958:
5957:
5883:
5869:
5863:
5837:
5836:
5803:
5802:
5781:
5776:
5775:
5751:
5743:
5703:
5702:
5663:
5662:
5617:
5616:
5545:
5544:
5507:
5506:
5483:
5482:
5463:
5462:
5400:3², 3³ and 3⁴.
5278:
5277:
5252:
5251:
5226:
5225:
5186:
5175:
5160:
5155:
5154:
5131:
5120:
5119:
5092:
5091:
5069:
5068:
5028:
5027:
5024:Newton's method
5006:
4959:
4958:
4923:
4912:
4911:
4881:
4880:
4861:
4860:
4831:
4830:
4803:
4798:
4797:
4772:
4771:
4752:
4751:
4727:
4722:
4721:
4702:
4701:
4668:
4649:
4648:
4623:
4622:
4601:
4584:
4583:
4582:By definition,
4549:
4548:
4499:
4498:
4449:
4448:
4409:
4408:
4373:
4362:
4361:
4351:
4327:
4326:
4287:
4286:
4256:
4255:
4236:
4235:
4207:
4206:
4181:
4180:
4135:
4134:
4133:. In any case,
4113:
4078:
4077:
4058:
4057:
4034:
4033:
3988:
3987:
3968:
3967:
3948:
3947:
3901:
3900:
3881:
3880:
3820:
3819:
3773:
3772:
3745:
3740:
3739:
3720:
3719:
3700:
3699:
3636:
3622:
3621:
3602:
3601:
3571:
3560:
3559:
3473:
3440:
3410:
3406:Groth16/ZkSnark
3401:
3272:
3267:
3113:
3091:
3069:
3040:
3030:
3024:
3023:
2996:15 60 90 60 15
2924:
2923:
2898:
2897:
2870:
2869:
2839:
2834:
2833:
2812:
2807:
2806:
2787:
2786:
2780:
2775:
2735:
2730:
2729:
2708:
2703:
2702:
2695:
2690:
2666:
2661:
2659:
2654:
2653:
2651:
2646:
2644:
2640:
2635:
2633:
2627:
2622:
2621:
2619:
2614:
2612:
2608:
2603:
2601:
2563:
2555:
2524:
2519:
2373:
2372:
2350:
2349:
2324:
2323:
2299:
2280:
2275:
2274:
2255:
2254:
2233:
2220:
2201:
2188:
2183:
2182:
2098:
2058:
2053:
1959:
1945:
1944:
1931:
1893:
1892:
1863:
1862:
1840:
1839:
1811:
1810:
1743:
1742:
1721:
1720:
1701:
1700:
1665:
1649:
1648:
1629:
1628:
1609:
1608:
1589:
1588:
1569:
1568:
1525:
1524:
1505:
1504:
1482:
1481:
1478:natural numbers
1458:
1457:
1414:
1408:
1406:
1353:
1339:
1338:
1325:
1304:
1298:
1296:
1245:
1231:
1230:
1213:
1207:
1205:
1174:
1168:
1166:
1149:
1143:
1141:
1097:
1071:
1070:
1039:
1033:
1031:
1000:
994:
992:
974:
968:
966:
934:
928:
926:
866:
852:
851:
795:
781:
780:
740:
726:
725:
685:
671:
670:
633:
632:
613:
612:
593:
592:
556:
542:
541:
505:
491:
490:
471:
470:
451:
450:
431:
430:
408:
395:
392:
356:
355:
333:
332:
329:spectral radius
276:
271:
266:
243:
240:
217:
214:
213:
209:
157:
155:
154:
149:
143:
139:
138:
134:
116:
115:
114:
107:
103:
54:
51:
46:
40:
29:
28:
21:
20:
12:
11:
5:
5992:
5990:
5982:
5981:
5976:
5971:
5961:
5960:
5956:
5953:
5951:
5949:
5948:
5947:
5946:
5945:
5944:
5931:
5919:
5913:
5910:
5907:
5904:
5901:
5898:
5895:
5892:
5889:
5886:
5881:
5878:
5875:
5872:
5866:
5862:
5859:
5856:
5853:
5850:
5847:
5844:
5834:
5822:
5819:
5816:
5813:
5810:
5788:
5784:
5772:
5771:
5770:
5769:
5768:
5747:
5715:
5712:
5690:
5687:
5684:
5681:
5678:
5674:
5670:
5650:
5647:
5644:
5641:
5638:
5634:
5630:
5627:
5624:
5602:
5599:
5594:
5591:
5588:
5584:
5580:
5577:
5574:
5569:
5566:
5563:
5560:
5555:
5552:
5532:
5529:
5526:
5523:
5520:
5517:
5514:
5490:
5470:
5428:
5427:
5426:
5425:
5424:
5423:
5420:
5419:
5416:
5413:
5402:
5401:
5398:
5395:
5384:
5383:
5380:
5377:
5366:
5365:
5362:
5359:
5340:
5339:
5338:
5337:
5336:
5335:
5332:
5291:
5288:
5285:
5265:
5262:
5259:
5239:
5236:
5233:
5222:
5221:
5220:
5219:
5218:
5207:
5201:
5198:
5195:
5192:
5189:
5184:
5181:
5178:
5172:
5167:
5163:
5138:
5134:
5130:
5127:
5116:
5105:
5102:
5099:
5076:
5056:
5053:
5050:
5047:
5044:
5041:
5038:
5035:
5026:) for solving
5003:
5002:
5001:
5000:
4999:
4998:
4997:is irrational.
4986:
4983:
4980:
4977:
4974:
4970:
4966:
4946:
4943:
4940:
4937:
4932:
4927:
4922:
4919:
4908:
4907:is irrational.
4896:
4892:
4888:
4868:
4858:
4846:
4842:
4838:
4816:
4813:
4810:
4806:
4785:
4782:
4779:
4759:
4748:
4734:
4730:
4709:
4695:
4681:
4678:
4675:
4671:
4667:
4664:
4660:
4656:
4636:
4633:
4630:
4608:
4604:
4600:
4597:
4594:
4591:
4580:
4568:
4565:
4562:
4559:
4556:
4536:
4533:
4530:
4527:
4524:
4521:
4518:
4515:
4512:
4509:
4506:
4486:
4483:
4480:
4477:
4474:
4471:
4468:
4465:
4462:
4459:
4456:
4446:
4434:
4431:
4428:
4425:
4422:
4419:
4416:
4396:
4393:
4390:
4387:
4382:
4377:
4372:
4369:
4353:
4352:
4340:
4337:
4334:
4314:
4311:
4308:
4305:
4302:
4298:
4294:
4284:
4279:
4278:
4277:
4275:
4263:
4243:
4221:
4218:
4215:
4194:
4191:
4188:
4168:
4165:
4162:
4159:
4156:
4152:
4148:
4145:
4142:
4120:
4116:
4112:
4109:
4106:
4103:
4100:
4097:
4094:
4091:
4088:
4085:
4065:
4041:
4021:
4018:
4015:
4012:
4009:
4005:
4001:
3998:
3995:
3975:
3955:
3935:
3932:
3929:
3926:
3923:
3920:
3917:
3914:
3911:
3908:
3888:
3868:
3864:
3860:
3857:
3854:
3851:
3848:
3845:
3842:
3839:
3836:
3833:
3830:
3827:
3807:
3804:
3801:
3798:
3795:
3792:
3789:
3786:
3783:
3780:
3758:
3755:
3752:
3748:
3727:
3707:
3687:
3684:
3681:
3678:
3675:
3672:
3669:
3666:
3663:
3660:
3657:
3654:
3649:
3646:
3643:
3639:
3635:
3632:
3629:
3609:
3589:
3584:
3581:
3578:
3574:
3570:
3567:
3504:
3503:
3493:
3477:fractal canopy
3472:
3441:
3439:
3436:
3409:
3402:
3400:
3397:
3396:
3395:
3394:
3393:
3392:
3391:
3330:
3320:
3319:
3299:
3271:
3268:
3266:
3263:
3262:
3261:
3260:
3259:
3258:
3257:
3256:
3255:
3254:
3253:
3252:
3251:
3139:
3136:
3130:
3125:
3122:
3117:
3108:
3103:
3100:
3095:
3086:
3081:
3078:
3073:
3067:
3061:
3055:
3052:
3049:
3046:
3043:
3039:
3034:
2967:
2964:
2961:
2958:
2955:
2952:
2949:
2946:
2943:
2940:
2937:
2934:
2931:
2911:
2908:
2905:
2877:
2854:
2851:
2846:
2842:
2819:
2815:
2794:
2779:
2776:
2774:
2771:
2742:
2738:
2715:
2711:
2694:
2691:
2689:
2686:
2684:
2682:
2681:
2679:
2678:
2677:
2676:
2675:
2664:
2657:
2649:
2642:
2638:
2631:
2625:
2617:
2610:
2606:
2599:
2595:map projection
2577:212.180.235.46
2559:
2547:map projection
2532:212.180.235.46
2530:in cm and km?
2523:
2520:
2518:
2515:
2514:
2513:
2512:
2511:
2479:
2478:
2477:
2454:
2453:
2452:
2424:
2423:
2422:
2410:
2407:
2404:
2401:
2398:
2395:
2392:
2389:
2386:
2383:
2380:
2369:
2357:
2337:
2334:
2331:
2322:the matrix of
2306:
2302:
2298:
2295:
2292:
2287:
2283:
2262:
2240:
2236:
2232:
2227:
2223:
2219:
2216:
2213:
2208:
2204:
2200:
2195:
2191:
2179:
2178:
2177:
2144:
2143:
2142:
2124:
2081:
2080:
2074:
2073:
2071:
2068:
2065:
2057:
2054:
2052:
2049:
2048:
2047:
2046:
2045:
2044:
2043:
2042:
2041:
1986:
1983:
1980:
1977:
1970:
1967:
1964:
1957:
1952:
1908:
1905:
1902:
1878:
1875:
1872:
1850:
1847:
1827:
1824:
1821:
1818:
1807:
1806:
1805:
1794:
1789:
1786:
1783:
1778:
1773:
1770:
1767:
1762:
1759:
1756:
1753:
1750:
1728:
1708:
1697:
1685:
1676:
1673:
1670:
1663:
1656:
1636:
1616:
1596:
1576:
1553:
1550:
1547:
1544:
1541:
1538:
1535:
1532:
1512:
1501:
1489:
1465:
1454:
1453:
1452:
1451:
1450:
1449:
1448:
1447:
1446:
1445:
1444:
1443:
1442:
1441:
1440:
1439:
1438:
1437:
1436:
1435:
1434:
1433:
1432:
1431:
1430:
1429:
1428:
1380:
1377:
1374:
1371:
1364:
1361:
1358:
1351:
1346:
1322:
1269:
1266:
1263:
1256:
1253:
1250:
1243:
1238:
1163:
1129:
1126:
1123:
1120:
1117:
1114:
1111:
1106:
1101:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
908:
907:
893:
890:
887:
884:
877:
874:
871:
864:
859:
836:
835:
833:
822:
819:
816:
813:
806:
803:
800:
793:
788:
778:
767:
764:
761:
758:
751:
748:
745:
738:
733:
723:
712:
709:
706:
703:
696:
693:
690:
683:
678:
662:to write down
656:
655:
640:
620:
600:
580:
577:
574:
567:
564:
561:
554:
549:
529:
526:
523:
516:
513:
510:
503:
498:
478:
458:
438:
423:
422:
407:
393:
391:
388:
387:
386:
385:
384:
366:
363:
343:
340:
325:
308:
307:
275:
272:
270:
267:
265:
264:
259:
254:
249:
241:
239:
238:
216:
207:
206:
204:
202:
201:
200:
199:
196:
193:
190:
184:
181:
178:
169:
166:
147:
145:
144:
140:
132:
130:
129:
113:
112:
104:
99:
97:
96:
95:
90:
85:
80:
75:
70:
65:
60:
52:
49:skip to bottom
47:
44:
42:
41:
32:
30:
15:
14:
13:
10:
9:
6:
4:
3:
2:
5991:
5980:
5977:
5975:
5972:
5970:
5967:
5966:
5964:
5954:
5952:
5943:
5939:
5935:
5932:
5917:
5908:
5905:
5902:
5896:
5893:
5890:
5887:
5884:
5879:
5876:
5873:
5870:
5864:
5860:
5857:
5854:
5851:
5848:
5845:
5842:
5835:
5820:
5817:
5814:
5811:
5808:
5786:
5782:
5773:
5767:
5764:
5760:
5756:
5750:
5746:
5741:
5740:
5739:
5735:
5731:
5713:
5710:
5685:
5679:
5676:
5672:
5668:
5645:
5642:
5636:
5632:
5628:
5625:
5622:
5600:
5597:
5592:
5586:
5582:
5575:
5572:
5567:
5564:
5561:
5558:
5530:
5527:
5524:
5521:
5518:
5515:
5512:
5504:
5488:
5468:
5460:
5459:
5458:
5455:
5451:
5450:
5445:
5441:
5438:changes when
5437:
5434:
5433:
5432:
5431:
5430:
5429:
5417:
5414:
5411:
5407:
5404:
5403:
5399:
5396:
5393:
5389:
5386:
5385:
5381:
5378:
5375:
5371:
5368:
5367:
5363:
5360:
5357:
5353:
5350:
5349:
5346:
5345:
5344:
5343:
5342:
5341:
5333:
5331:
5328:
5324:
5323:
5318:
5314:
5310:
5309:
5308:
5305:
5286:
5260:
5237:
5234:
5231:
5224:In practice (
5223:
5205:
5199:
5196:
5193:
5190:
5187:
5182:
5179:
5176:
5170:
5165:
5161:
5153:
5152:
5136:
5132:
5128:
5125:
5117:
5103:
5100:
5097:
5089:
5088:
5074:
5054:
5051:
5048:
5045:
5042:
5039:
5036:
5033:
5025:
5021:
5020:
5019:
5015:
5011:
5008:
5007:
4981:
4978:
4972:
4968:
4964:
4941:
4930:
4920:
4917:
4909:
4894:
4890:
4886:
4866:
4859:
4844:
4840:
4836:
4814:
4811:
4808:
4804:
4783:
4780:
4777:
4757:
4749:
4732:
4728:
4707:
4699:
4696:
4679:
4676:
4673:
4669:
4665:
4662:
4658:
4654:
4634:
4631:
4628:
4606:
4602:
4598:
4595:
4592:
4589:
4581:
4566:
4563:
4560:
4557:
4554:
4534:
4531:
4528:
4522:
4519:
4513:
4510:
4504:
4484:
4481:
4478:
4472:
4469:
4463:
4460:
4454:
4447:
4429:
4426:
4420:
4417:
4414:
4391:
4380:
4370:
4367:
4359:
4358:
4357:
4356:
4355:
4354:
4338:
4335:
4332:
4309:
4306:
4300:
4296:
4292:
4282:
4276:
4261:
4241:
4219:
4216:
4213:
4192:
4189:
4186:
4163:
4160:
4154:
4150:
4146:
4143:
4140:
4118:
4114:
4110:
4107:
4104:
4098:
4095:
4089:
4083:
4063:
4055:
4039:
4016:
4013:
4007:
4003:
3999:
3996:
3993:
3973:
3953:
3930:
3924:
3921:
3918:
3915:
3912:
3909:
3906:
3886:
3866:
3862:
3855:
3852:
3849:
3843:
3837:
3831:
3828:
3825:
3802:
3796:
3793:
3787:
3784:
3781:
3756:
3753:
3750:
3746:
3725:
3705:
3682:
3676:
3673:
3667:
3664:
3661:
3655:
3647:
3644:
3641:
3637:
3630:
3627:
3607:
3582:
3579:
3576:
3572:
3557:
3556:
3555:
3554:
3551:
3547:
3546:
3540:
3537:
3535:
3531:
3527:
3523:
3519:
3515:
3511:
3498:
3494:
3488:
3484:
3483:
3480:
3478:
3470:
3466:
3462:
3458:
3454:
3450:
3446:
3442:
3437:
3435:
3434:
3430:
3426:
3421:
3417:
3413:
3407:
3403:
3398:
3390:
3387:
3383:
3379:
3378:flash traders
3375:
3371:
3370:
3369:
3365:
3361:
3358:
3354:
3350:
3346:
3342:
3338:
3334:
3333:Pump and dump
3331:
3328:
3324:
3323:
3322:
3321:
3318:
3314:
3310:
3306:
3305:Pump and dump
3302:
3301:
3300:
3297:
3296:
3292:
3288:
3283:
3279:
3278:
3269:
3264:
3250:
3246:
3242:
3237:
3236:
3235:
3231:
3227:
3223:
3220:
3219:
3218:
3214:
3210:
3206:
3205:
3204:
3200:
3196:
3192:
3189:
3188:
3187:
3183:
3179:
3175:
3171:
3167:
3163:
3162:
3161:
3157:
3153:
3137:
3134:
3123:
3120:
3101:
3098:
3079:
3076:
3065:
3053:
3050:
3047:
3044:
3041:
3037:
3020:
3019:
3018:
3017:
3013:
3009:
2982:
2979:
2965:
2962:
2959:
2956:
2953:
2950:
2947:
2944:
2941:
2938:
2935:
2932:
2929:
2909:
2906:
2903:
2895:
2891:
2875:
2866:
2852:
2849:
2844:
2840:
2817:
2813:
2792:
2783:
2772:
2770:
2769:
2765:
2761:
2756:
2740:
2736:
2713:
2709:
2700:
2692:
2687:
2685:
2680:
2674:
2671:
2596:
2592:
2588:
2587:
2586:
2582:
2578:
2573:
2569:
2568:
2567:
2562:
2558:
2557:-- Verbarson
2553:
2548:
2544:
2543:
2542:
2541:
2537:
2533:
2529:
2521:
2516:
2510:
2506:
2502:
2498:
2494:
2493:
2492:
2488:
2484:
2480:
2476:
2472:
2468:
2464:
2463:
2462:
2459:
2455:
2451:
2447:
2443:
2439:
2438:
2437:
2433:
2429:
2425:
2405:
2402:
2399:
2393:
2387:
2384:
2381:
2370:
2355:
2335:
2332:
2329:
2321:
2320:
2304:
2300:
2296:
2293:
2290:
2285:
2281:
2260:
2238:
2234:
2230:
2225:
2221:
2217:
2214:
2211:
2206:
2202:
2198:
2193:
2189:
2180:
2176:
2172:
2168:
2164:
2160:
2159:
2158:
2154:
2150:
2145:
2141:
2137:
2133:
2129:
2125:
2122:
2121:
2120:
2116:
2112:
2108:
2102:
2097:
2096:
2095:
2094:
2090:
2086:
2079:
2078:
2077:
2072:
2069:
2066:
2063:
2062:
2061:
2055:
2050:
2040:
2036:
2032:
2028:
2024:
2023:
2022:
2018:
2014:
2009:
2008:
2007:
2003:
1999:
1984:
1981:
1978:
1975:
1955:
1950:
1941:
1937:
1934:
1929:
1928:
1927:
1924:
1906:
1903:
1900:
1876:
1873:
1870:
1848:
1845:
1822:
1816:
1808:
1792:
1787:
1784:
1781:
1776:
1771:
1768:
1765:
1760:
1754:
1748:
1741:
1740:
1726:
1706:
1698:
1683:
1661:
1654:
1634:
1614:
1594:
1574:
1566:
1548:
1545:
1542:
1536:
1533:
1530:
1510:
1502:
1487:
1479:
1463:
1455:
1427:
1423:
1421:
1413:
1411:
1404:
1403:
1402:
1398:
1394:
1378:
1375:
1372:
1369:
1349:
1344:
1335:
1331:
1328:
1323:
1319:
1318:
1317:
1313:
1311:
1303:
1301:
1294:
1293:
1292:
1288:
1284:
1267:
1264:
1261:
1241:
1236:
1228:
1227:
1226:
1222:
1220:
1212:
1210:
1203:
1202:
1201:
1197:
1193:
1189:
1188:
1187:
1183:
1181:
1173:
1171:
1164:
1162:
1158:
1156:
1148:
1146:
1127:
1124:
1121:
1118:
1115:
1109:
1104:
1094:
1088:
1085:
1082:
1068:
1067:
1066:
1062:
1058:
1054:
1053:
1052:
1048:
1046:
1038:
1036:
1029:
1028:
1027:
1023:
1019:
1015:
1014:
1013:
1009:
1007:
999:
997:
989:
988:
987:
983:
981:
973:
971:
963:
962:
961:
957:
953:
949:
948:
947:
943:
941:
933:
931:
923:
922:
921:
920:
916:
912:
906:
905:
904:
891:
888:
885:
882:
862:
857:
849:
845:
841:
834:
820:
817:
814:
811:
791:
786:
779:
765:
762:
759:
756:
736:
731:
724:
710:
707:
704:
701:
681:
676:
669:
668:
667:
665:
661:
654:
653:
652:
638:
618:
598:
578:
575:
572:
552:
547:
527:
524:
521:
501:
496:
476:
456:
436:
428:
421:
420:
419:
417:
413:
405:
401:
398:
394:
389:
383:
380:
364:
361:
341:
338:
330:
326:
324:
320:
316:
312:
311:
310:
309:
306:
302:
298:
293:
292:
291:
290:
286:
282:
273:
268:
263:
260:
258:
255:
253:
250:
248:
245:
236:
232:
231:
230:
229:
228:
222:
220:
212:
205:
197:
194:
191:
188:
187:
185:
182:
179:
176:
175:
170:
167:
164:
163:
162:
160:
142:
128:
127:
126:
119:
110:
106:
105:
102:
94:
91:
89:
88:Miscellaneous
86:
84:
81:
79:
76:
74:
71:
69:
66:
64:
63:Entertainment
61:
59:
56:
50:
39:
37:
25:
19:
5950:
5934:GalacticShoe
5758:
5754:
5748:
5744:
5730:GalacticShoe
5503:OEIS:A108414
5447:
5443:
5439:
5435:
5409:
5405:
5391:
5387:
5373:
5369:
5355:
5351:
5320:
5313:GalacticShoe
5010:GalacticShoe
3966:in terms of
3543:
3541:
3538:
3533:
3529:
3525:
3521:
3517:
3513:
3509:
3507:
3474:
3468:
3464:
3460:
3456:
3452:
3448:
3444:
3438:September 30
3422:
3418:
3414:
3411:
3399:September 29
3327:MetaTrader 4
3298:
3284:
3280:
3273:
3265:September 28
3152:Double sharp
3004:
2993:20 60 60 20
2980:
2893:
2889:
2867:
2784:
2781:
2773:September 27
2757:
2696:
2688:September 26
2683:
2525:
2517:September 23
2496:
2368:is zero, and
2162:
2127:
2106:
2082:
2075:
2059:
2051:September 22
1939:
1935:
1932:
1564:
1419:
1409:
1333:
1329:
1326:
1309:
1299:
1218:
1208:
1179:
1169:
1154:
1144:
1044:
1034:
1005:
995:
979:
969:
939:
929:
909:
847:
843:
839:
837:
663:
659:
657:
426:
424:
415:
411:
409:
403:
399:
396:
390:September 20
277:
269:September 19
257:Village pump
224:
223:
218:
215:
203:
172:
158:
156:
141:
122:
121:
117:
77:
33:
5382:2¹ and 2².
4285:Proof that
3879:, which is
3512:) for each
3447:) for each
3345:Uptick rule
3226:Georgia guy
3195:Georgia guy
3008:Georgia guy
2428:Tito Omburo
1321:definition.
297:Tito Omburo
262:Help manual
225:Main page:
123:Main page:
78:Mathematics
5963:Categories
5415:(4 terms):
5397:(3 terms):
5379:(2 terms):
4407:, and let
4232:1}" /: -->
3698:. Because
2348:minors of
2070:C=(0,1,0).
2067:B=(1,0,0),
2064:A=(1,1,0),
844:sufficient
660:sufficient
412:definition
68:Humanities
5955:October 2
5481:for each
5361:(1 term):
3382:exchanges
3337:Bear raid
2990:15 30 15
2628:= 160,000
2620:. So for
2128:dependent
252:Help desk
242:See also:
235:wikilinks
58:Computing
5891:4.197225
5885:2.373852
5877:5.197225
5615:, while
5412:=8 to 11
4957:implies
4621:. Since
4579:as well.
4360:Suppose
4209:1}": -->
3542:Thanks,
3475:Drawing
1410:Remsense
1300:Remsense
1209:Remsense
1170:Remsense
1145:Remsense
1035:Remsense
996:Remsense
970:Remsense
930:Remsense
840:Question
247:Teahouse
109:WP:RD/MA
101:Shortcut
93:Archives
73:Language
5763:Lambiam
5442:is the
5408:=4 for
5394:=5 to 7
5390:=3 for
5376:=3 to 4
5372:=2 for
5354:=1 for
5317:Lambiam
5304:Lambiam
4052:is the
3412:Hello,
3386:Lambiam
2670:Lambiam
2458:Lambiam
1923:Lambiam
848:shorter
379:Lambiam
83:Science
5449:cmɢʟee
5322:cmɢʟee
4032:where
3545:cmɢʟee
3516:where
3451:where
3343:, and
3309:RDBury
3241:RDBury
3222:RDBury
3209:RDBury
3191:RDBury
3178:RDBury
2728:and B∈
2575:wide.
2501:HOTmag
2497:Thanks
2467:HOTmag
2442:HOTmag
2167:HOTmag
2163:Thanks
2132:HOTmag
2111:CiaPan
2101:HOTmag
2085:HOTmag
2031:HOTmag
2013:RDBury
1998:HOTmag
1393:HOTmag
1283:HOTmag
1192:HOTmag
1057:HOTmag
1018:HOTmag
952:HOTmag
911:HOTmag
186:Note:
5315:and @
4547:, so
4217:: -->
3899:when
2668:. --
2591:scale
2561:edits
2528:scale
315:RJFJR
281:RJFJR
174:tilde
16:<
5938:talk
5734:talk
5454:τaʟκ
5364:1¹.
5327:τaʟκ
5276:and
5235:<
5090:Set
5014:talk
4497:and
3550:τaʟκ
3528:and
3463:and
3429:talk
3364:talk
3313:talk
3291:talk
3245:talk
3230:talk
3213:talk
3199:talk
3182:talk
3156:talk
3012:talk
2987:6 6
2892:and
2764:talk
2660:= 2
2589:The
2581:talk
2536:talk
2505:talk
2487:talk
2471:talk
2446:talk
2432:talk
2171:talk
2153:talk
2136:talk
2115:talk
2089:talk
2035:talk
2017:talk
2002:talk
1891:and
1809:For
1397:talk
1287:talk
1196:talk
1061:talk
1022:talk
956:talk
915:talk
319:talk
301:talk
285:talk
4750:If
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2426:-
1607:or
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2015:(
2000:(
1985:?
1982:B
1976:A
1969:f
1966:e
1963:d
1956:=
1951:C
1940:C
1938:+
1936:B
1933:A
1907:x
1904:+
1901:1
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1655:B
1635:B
1615:C
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1552:)
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1543:B
1540:(
1537:f
1534:=
1531:A
1511:A
1464:+
1420:论
1395:(
1379:.
1376:B
1370:A
1363:f
1360:e
1357:d
1350:=
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1332:+
1330:B
1327:A
1310:论
1285:(
1268:B
1262:A
1255:f
1252:e
1249:d
1242:=
1237:C
1219:论
1194:(
1180:论
1155:论
1128:C
1125:+
1122:B
1119:=
1116:A
1110:,
1105:+
1100:R
1092:)
1089:C
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1080:(
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1020:(
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980:论
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940:论
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821:.
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737:=
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711:.
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705:+
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682:=
677:A
639:C
619:B
599:A
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576:+
573:B
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563:e
560:d
553:=
548:A
528:C
525:+
522:B
515:f
512:e
509:d
502:=
497:A
477:A
457:C
437:B
404:C
402:+
400:B
397:A
365:,
362:1
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339:1
317:(
299:(
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