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add it to a different wiki page. 4) The section titled "Miscellaneous" has an existing wiki page on harmonic numbers. Delete this section and add it to the wiki page on harmonic numbers. 5) The links for the citation to Graham et. al. either do not work or are irrelevant to the citation. Remove the links.
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Your reference to the rest of the article is a fallacy, as "positive integer" is used once in a formula where excluding zero is fundamental, while "natural number" is used three time, without indicating whether zero is included, except for the third formula that remains true if the term of index 0 is
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reads "This article may require cleanup to meet
Knowledge's quality standards." When I edit the page, the banner goes away. I tried editing the summation page to fit the wiki encyclopedia style. I also revised the grammar, spelling, and references for correctness and clarity. D Lazard likes his(her)
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I KEEP removing these identities and someone keeps putting them right back in without checking correctness. Distributivity and factorization on the list are INVALID. If it doesnt work for a binomial why would anyone assume it worked for an arbitrary series? Hate fighting idiots on wikipedia. If you
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Here are some more edits: 1) The "Formal
Definitions" section does not define recursion. 2) The last formula in the section titled "Summation index in exponents" is a partial proof. Remove the derivation. 3) The section titled "Growth rates" is irrelevant to this page. Delete the entire section and
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I am a dumb, ignorant, old guy going back to school to learn math. So, I read this article and find the statement "It is possible to sum fewer than 2 numbers". Really? That seems, to me, anyway, to violate the logic of a definition of a sum; a sum means we are adding one value to another value
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The sentence, as it is currently, is absolutely not ambiguous, as I do not know anybody who understand "the 100 first natural numbers" as not containing 100. Moreover, in the case of a doubt, this is clarified by the formula that follows. So, the unneeded use of a technical terminology that you
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1. Many definitions, including the official standard ISO 80000-2, include 0 in the natural numbers. "Natural numbers" may or may not include 0, while "positive integers" always excludes 0. A more precise term is preferable to a less precise one. Why use an ambiguous term when an unambiguous one
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You deal with sums of a single number all the time. Every time you go to a store and buy a single item, there's a line on the receipt that says "total" (er, well, "subtotal") with just the price of that one item, right? So the sum of a single item is really not an impossible concept—it's a very
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says "The lead should, as much as possible, be accessible to a general reader, so specialized terminology should be avoided". Here "positive integer" is a (mathematical) specialized terminology, as "positive" and "integer" are taught to kids a long time after they know natural
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says "The lead should, as much as possible, be accessible to a general reader, so specialized terminology should be avoided". Here "positive integer" is a (mathematical) specialized terminology, as "positive" and "integer" are taught to kids a long time after they know natural
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A sum of zero numbers is similar. Imagine that you have a bank account into which you make no deposits for a certain month. At the end of the month you will get a statement from the bank with a line that says something like, "Total deposits $ 0.00." That's a sum of no numbers!
429:(or more values). Why would we even bother to try to denote this impossible concept of a sum of one or zero values? That just does not make sense to me. Wouldn't we just instead say that the starting conditions "m = n" or "m : -->
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How about replacing "summation of the first 100 natural numbers" with "summation of natural numbers from 1 to 100"? However, in the sentence immediately after it, it says "1 + 2 + 3 + ... + 100", so I think it's clear even as it is
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Which identities are wrong and what are the correct identities? Note that in the comments, "distributivity", ... do not mean that the identity makes the property explicit, but rather that this is used for proving the identity.
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I disagree with that "should have been". Your perspective is one derived from programmers (is it not?) who initiated their own convention long after mathematics had theirs. Youre assuming one is wrong
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Its probably best not to think of it as literal adding. Rather, think of it is a convention. Something formal mathematics has been forced to accept for consistency. Its not without its logic.
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youve accepted the other. It's a perfect example of bias. Am I wrong? Can you justify precisely why the convention *should* have been different without presupposing the other?
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are weak at math and dont know what youre talking about, and wont even research, then quit contributing. Simple. Im starting to think its malice rather than stupidity.
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here, as your change has been reverted by two different editors, none of which being the author of the disputed sentence. On the other hand there is a clear problem of
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ISO is not and has never been a standard for mathematics. It is not an official standard, as ISO is a private company. However, ISO is commonly used as a standard in
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2. The rest of the article (see the section titled "Powers and logarithm of arithmetic progressions") also uses the convention of including 0 in the natural numbers.
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Right; this is corrected now. As a general rule summation expressions would be simpler if the upper limit in a summation would have been the first value
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The sum of 1 from m to n is n - m + 1, not n - m. A trivial example, sum 1 from 1 to 10, the answer is not (10 - 1 = 9), it is (10 - 1 + 1 = 10).
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n" are just not allowed or undefined, in the same manner as we might say "any value divided by zero is undefined"? Please explain.
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Which relationship have in mind? For the relationship between repeated addition and multiplication, see the second paragraph of
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version. The first sentence has a personal pronoun referring to a sum. Keep reading each sentence...more errors follow.
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ISO is an independent, non-governmental international organization with a membership of 166 national standards bodies.
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has insisted on reverting this constructive edit, without providing a justification. Their actions suggest
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to include rather than the last value to include, but it's too late to change that convention. Note that
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2. The term "natural number" (as opposed to simply "number") is no less "technical" than "integer".
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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I'll look at the information to see if you're correct, should I have time to do that.
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This seems like a trivial thing, but seems to be incorrect in the listing.
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It is also used as a standard in chemistry, physics, and mathematics. See
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This is my first ever
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Nevermind. It would appear that the IP was vandalizing the article
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Can you please explain why you removed a bunch of information?
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The sentence, as it is currently, is absolutely not ambiguous
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ambiguous, since "natural numbers" may or may not include 0.
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It is not an official standard, as ISO is a private company.
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Relationship between summation and repeated multiplication
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Defining a relationship between these two will be good.
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Change "natural numbers" to "positive integers" in lede
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561:(
536::
532:@
528::
524:@
520::
516:@
499:(
483:(
479:—
466:(
444:(
404:(
381:(
375:m
371:n
367:m
363:n
359:n
355:n
337:(
303:.
202::
128:1
125::
58:.
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