# Tagged Questions

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### Who invented measure theory?

Suddenly, i wonder who invented measure theory. I thought Lebesgue had invented it, but i think too many deep results were found in a very short time after Lebesgue introduced abstract integral and ...
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### Should the notion of continuity, usually ascribed to Cauchy, be ascribed to Leibniz?

In his text, Deleuze and the History of Mathematics, Simon Duffy writes: Leibniz also thought the following to be a requirement to continuity: "When the difference between two instances in a ...
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### History of Calculus

Newton/ Leibniz invented calculus on approximately 1680's. Cauchy/Weierstrauss defined the $\epsilon - \delta$ definition of a limit in approximately 1820's. So how did they define derivatives? I ...
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### Who came up with the $\varepsilon$-$\delta$ definitions and the axioms in Real Analysis?

I've seen a lot of definitions of things like boundary points, accumulation points, continuity, etc, and axioms of the real numbers. But I have a hard time accepting these as "true" definitions or ...
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### Decimal system history

Today, "numbers" usually refer to real numbers and are most commonly conceptualized as consisting of all possible infinite decimal expansions (or binary expansions, etc). When did this way of thinking ...
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### Is mathematical history written by the victors?

The question is the title of a recent piece in the Notices of the American Mathematical Society, by twelve authors (of which I am one). The contention is that traditional history of mathematics is ...
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### history of the contraction mapping technique

If $|f(x)-f(y)| \leq k|x-y|$ for all $x,y$ then $f$ is Lipschitz with constant $k$, if $k<1$ then $f$ is called a contraction mapping. The beautiful result that a fixed point is associated to a ...
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### Who was the first to prove $\lim_{x \to 0} \frac{\sin{x}}{x}=1$?

Who was the first to prove $\lim_{x \to 0}\frac{\sin{x}}{x}=1$?
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### A curious theorem by Peano

Let $f$ be defined on $[a,b]$ and there differentiable. Show that for every $\epsilon>0$ there exists a partition $\, a=a_0<a_1<...<a_n=b \,$ of $\,[a,b] \,$ so that \left|\frac ...
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### Gray's “Plato's Ghost” - a curious mistake

I am currently reading Jeremy Gray's "Plato's Ghost", and I run into the following passage (Chapter 5, page 332). The point is, it seems to me that it contains two very elementary mistakes that feel ...
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### Is the theory of dual numbers strong enough to develop real analysis, and does it resemble Newton's historical method for doing calculus?

I've been interested in non-standard analysis recently. I was reading up on it and noticed the following interesting comment on the Wikipedia page about hyperreal numbers, right after giving an ...
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### Who is responsible for the analytical/topological proof of FTA?

The fundamental theorem of algebra asserts: Theorem Let $P$ be a polynomial of degree $\geq 1$ in $\Bbb C$. Then there exists a $z_1\in\Bbb C$ such that $P(z_1)=0$. The proof sketch goes as ...
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### Old versus New enunciation of Taylor's Theorem.

I am studying from Spivak' Calculus, and he states Taylor's Theorem as follows: THEOREM Let $f',\cdots,f^{(n+1)}$ be defined on $[a,x]$ and let $R_{n,a}(x)$ be defined by ...
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### History of the construction of $\mathbb{R}$

When did the constructions of Reals take place? What is the latest construction the one due to Cantor (by Cauchy Sequences) or the Dedekind? I ask because the trustful reference (baby Rudin) that I ...