animated
发表于 2025-3-23 11:58:43
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Ceramic
发表于 2025-3-23 15:14:37
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影响带来
发表于 2025-3-23 22:02:14
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jarring
发表于 2025-3-24 00:12:08
,Axioms for ℝ—in which we invent Arithmetic, Order our numbers and Complete our description of the rs that they are consequences of even more basic assumptions— namely, our axioms. To make the following exposition more palatable, we shall present the defining axioms in three measured helpings. We shall also enlist the aid of our friends Alice, Tweedledee and Tweedledum… so, to work!
广告
发表于 2025-3-24 02:40:34
,The Real Numbers—in which we find holes in the number line and pay the price for repairs,ht, depending on whether . is negative or positive; and our (semi-formal) definition of a rational number is any number which can be expressed as the ratio between two integers, ., with the proviso that m is not zero.
licence
发表于 2025-3-24 07:50:10
,Psychomotorische Erregungszustände,d be no such thing as an infinite set of real objects. However, mathematicians do not, in general, see this as a problem, and confidently assume that infinite sets (even if they are only sets of . objects) can be handled with safety.
乐章
发表于 2025-3-24 10:40:52
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LAVE
发表于 2025-3-24 15:05:45
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scrape
发表于 2025-3-24 22:33:08
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ASTER
发表于 2025-3-25 02:03:50
,Permutations—in which ALICE is transformed,m it an appreciation that many of the concepts discussed in the main stream with reference to numbers are really of much wider applicability. The concepts we have in mind are factorisation, uniqueness, well-defined and equivalence classes.