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Titlebook: Analysis I; Third Edition Terence Tao Textbook 20161st edition The Editor(s) (if applicable) and The Author(s), under exclusive license to

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41#
發(fā)表于 2025-3-28 16:52:08 | 只看該作者
42#
發(fā)表于 2025-3-28 22:01:23 | 只看該作者
https://doi.org/10.1007/978-94-011-5318-8al numbers. However, unlike our work in constructing the integers (where we eventually replaced formal differences with actual differences) and rationals (where we eventually replaced formal quotients with actual quotients), we never really finished the job of constructing the real numbers, because
43#
發(fā)表于 2025-3-29 01:20:11 | 只看該作者
https://doi.org/10.1007/978-3-662-68353-8number .. to each natural number .. We then did various things with these functions from . to ., such as take their limit at infinity (if the function was convergent), or form suprema, infima, etc., or computed the sum of all the elements in the sequence (again, assuming the series was convergent).
44#
發(fā)表于 2025-3-29 05:39:38 | 只看該作者
Conclusion and Recommendations for Actionusing limits, in contrast to the geometric definition of derivatives, which uses tangents. The advantage of working analytically is that (a) we do not need to know the axioms of geometry, and (b) these definitions can be modified to handle functions of several variables, or functions whose values ar
45#
發(fā)表于 2025-3-29 10:12:14 | 只看該作者
https://doi.org/10.1007/978-3-662-68353-8 current chapter. More precisely, we will turn to the ., the integral of a function on a fixed interval, as opposed to the ., otherwise known as the antiderivative. These two are of course linked by the ., of which more will be said later.
46#
發(fā)表于 2025-3-29 14:28:54 | 只看該作者
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