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numbers 10^4, 10^8, and so on). A google search of the specific citation turns up Hindu twitter accounts and websites, and nothing scholarly. This exact citation was, I believe, copied directly from "Hindupedia", although that page does not really assert what this sentence asserts. Certainly none of it appears to support the statement that the text makes use of "mathematical decimal fractions", which also conflicts with the information in this article, which puts the first use of decimal fractions around a thousand years after that. But I do not feel strongly enough about it to undo your reversion.
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679:. So, saying that infinite decimals are an extension of finite decimals is coherent with history and with the level of abstraction needed to understand the concepts. Saying, as you suggest, that finite decimals are only a special case of infinite decimals, is logically correct, but, IMO, a form of pedantry, consisting of asking the reader to understand complicate things before using more simpler and more useful things.
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The thing is, the finite decimals are not about representing numbers exactly (and since you brought up history, they never have been about representing numbers exactly). They're about representing numbers approximately. The only ones they can represent exactly are those rationals with a denominator
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IMO, it suffices to replace "Generally" with "Originally and in most uses". Even in mathematics, infinite decimals are not really used, except for the study of the cardinality of the real numbers. I agree that "Generally" is confusing, as if may be wrongly understood as "most decimals are finite".
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Nobody is saying that finite decimals represent all numbers exactly. They represent decimal fractions exacly, and are widely used to approximate real numbers. Infinite decimals are essentially used only for the study of the cardinality of the continuum. So the main case is definitively the finite
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to your suggestion. Basically, a (finite) decimal is a numeral that allows representing some numbers, namely the decimal fractions. Infinite decimals are not numerals, as most of them cannot be written; they may be viewed as increasing sequences or series, and have a very different nature. Finite
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Hi. Yes, I did check it. It's a primary source, actually, of a hymn. I did search google books/scholar for "Atharvaveda" + decimal fractions (with and without a space in "Atharva Veda") and it turned up nothing beyond a couple of references to place value (related to the text having words for the
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I actually think the first sentence should just be removed, and the second sentence should not talk of an "extension" but rather should say that the expansion may be infinite. Then the third sentence should change to saying that a "terminating decimal" is one that can be expressed with a finite
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So I think it's misleading (and by the way unsourced) to call out the finite decimals as a special class. It's particularly dangerous given that many readers of this article are already foggy on the difference between numbers and numerals, and already think there's something special about base
769:โ in your own textbook you can make up whatever neologism you like. Knowledge should stick to standard terminology where it exists (and in the rare exceptional case where a non-standard term is needed for whatever reason, should be extremely clear to point that out).
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Now, to the extent that the desk's width is completely well-defined (which of course it probably isn't, but let's go with it for now), if you had better and better measurement tools, you could keep going, adding more and more digits, without any obvious fixed limit.
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language that I think is currently problematic. I'm happy to rethink it to avoid any active suggestion that the finite decimals are a special case. I just don't think we should walk readers down a garden path towards the idea that they're the main case.
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But surely we don't want to go onto a digression about actual versus potential infinity, certainly not in the lead, and probably not in this article at all. It's an almost
Scholastic distinction that has little to do with the topic given by the title.
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infinite expansions have been known much longer, and schoolchildren are familiar with the idea that you can do decimal division of 1 by 3 and it keeps spitting out 3s, and the more advanced ones will know that there's an algorithm for computing (say)
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means something like "I can measure the desk's width to a precision of roughly 0.1 cm, and when I do that it comes out 90.2. It's probably between 90.15 and 90.25, but I'm not signing over my firstborn in case it's a little outside that range."
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I wasn't suggesting that we should add that term to the article. I was pointing out that the term "decimal fraction" does not in itself capture the restriction to finite decimals, and proposing a term D.Lazard could have used in this
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Consider adding the following text to the intro of the article, as discussing the limitations of the base 10 system would be beneficial for readers curious about such information regarding it. The text is in brackets.
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case, except possibly for specialists of mathematical logic. IMHO, infinite decimals should not be taught before college. In any case, they should not be taught to people who do not master approximations.
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So "generally" there's no actual fixed finite number of digits to which a decimal should be expanded. The exception would be if you had some reason to believe the exact answer were of the form
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representing another number in another base. It is true that 10 is a numeral that represents a base in the base itself. It seems that you confuse "numeral 10" with "base 10".
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Also I didn't say finite decimals were unimportant. What I said, or at least what I meant, is that the numbers exactly represented by finite decimals (the ones of the form
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A couple more remarks: Your claims about the limited applications that infinite decimals are "used" for seem to apply only to actually infinite decimal expansions.
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It's true that finite decimals represent decadic fractions exactly, but those are fairly unimportant and definitely not the motivation for the notation.
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whose only prime factors are 2 and 5, which is not a particularly interesting class of numbers in either mathematics or science (oh, I expect there's
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Where does this "generally" come from? I think the most common usage is actually as an approximation to some measured quantity. For example
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One test example: We should probably point out early that 2.3 means something different from 2.30, as the latter implies higher precision.
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I am not suggesting that we should lead heavily with infinite decimals. I do think we should remove the language that I've called out. --
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Generally, a decimal has only a finite number of digits after the decimal seperator. However, the decimal system has been extended to
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number of digits (of course it isn't really finite, it just starts becoming all zeroes, but we can leave that out in this spot). --
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For precision you should say something like "decadic fraction" rather than decimal fraction, as an infinite decimal arguably
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i started the topic because, in the context of numeral systems, there isn't really such a thing as "base 10". in
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interesting mathematics you can do with them, but whatever it is, I doubt it's very relevant to this discussion).
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I see your point, and thanks for informing me. Disregard the edit suggestion.
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I suggest to add a subsection on conversion to numbers with different bases
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