Questions tagged [real-analysis]

For questions about the history of calculus and its theoretical foundations, including topics such as continuity, differentiability, and infinite series. Related topics include questions on the history of measure theory, and some aspects of general topology and classical descriptive set theory.

For questions about the history of calculus and its theoretical foundations, including topics such as different constructions and axiomatizations of the reals, continuity, differentiability, infinite series, Lebesgue measurability, and the Baire property. Related topics include questions on the history of the theory of differential equations, functional analysis, measure theory, and some aspects of general topology and classical descriptive set theory.

Consider also the tag.

93 questions
12
votes
2 answers

Who was the first to prove the mean value theorem?

Who was the first to prove the mean value theorem, i.e., the existence of an intermediate point where the slope equals the average slope over the interval?
Mikhail Katz
  • 5,743
  • 18
  • 39
10
votes
4 answers

Historically, what led to the question of the validity of interchange of limit operations?

It seems G. H. Hardy once wrote that "The problem of deciding whether two given limit operations are commutative is one of the most important in mathematics". I was wondering what led to the need to formulate the question of when the limit…
A.D.
3
votes
0 answers

Why does Rolle get its own theorem?

The importance of Rolle's theorem lies in the fact that it's used to prove the mean value theorem, which is a central result of analysis, eventually leading to the fundamental theorem of calculus. But if I compare the usual proof of the mean value…
Vercassivelaunos
0
votes
1 answer

How did Dedekind arrive at the completeness of real numbers?

Reading Dedekind original manuscript (https://archive.org/details/essaysintheoryof00dedeuoft) it seems that he was after formalizing the completeness of the real numbers, which was known to him as the continuity of real numbers. Formalizing the…
abk
  • 163
  • 4
-1
votes
1 answer

Why the scaling rule $\delta(a x)=\frac1{|a|}\delta(x)$ was historically adopted?

It seems to me that it would be more natural to consider Dirac Delta as a piecewise-defined function, as described here, with the scaling rule $\delta (ax)=\delta(x)$. This way we keep all the integral transforms properties of delta function, and…
Anixx
  • 652
  • 5
  • 13