BULK 发表于 2025-3-21 19:01:26
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What Are Proofs, and Why Do We Write Them?,le “All rational numbers are positive” and “There is a real number . such that .” are false statements. Some sentences like “Green is nice” or “Authenticity runs hot” are too ambiguous, a matter of opinion, or are just plain nonsense and cannot be said to be true or false, so mathematicians would noGenistein 发表于 2025-3-22 05:24:08
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Limits,and, indeed, the central concept of Analysis. In particular, if . is a function defined on an open interval containing ., then . has limit . at . if the values of .(.) get closer and closer to . as . approaches .. In order to prove theorems about limits, one needs a rigorous definition of limit whicERUPT 发表于 2025-3-22 16:20:34
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Derivatives,ormous number of applications. Not only does it provide a great tool for understanding the behavior of functions, but it also has applications to a very wide range of other fields, most notably Physics, Engineering, Chemistry, Biology, and Economics. In particular, being able to use the derivative tlesion 发表于 2025-3-23 00:53:08
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Sequences of Functions,and subsequences . of such a sequence. If instead of requiring the terms of the sequence .. to be constants, the .. were allowed to depend on the value of a variable as in ..(.), then the sequence is a sequence of functions. Thus, for each value of ., if all the functions ..(.) are defined at ., the