Nonstandard analysis is a way of doing calculus and analysis with infinitesimals. The historical approach of Leibniz, Euler, and others to infinitesimal calculus was gradually replaced by epsilon, delta techniques in the context of a real continuum, in the 19th century. It was not until the 1960s ...

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A remark of Connes

In an interview (at http://www.alainconnes.org/docs/Inteng.pdf) Connes remarks that I had been working on non-standard analysis, but after a while I had found a catch in the theory.... The point ...
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How helpful is non-standard analysis?

So, I can understand how non-standard analysis is better than standard analysis in that some proofs become simplified, and infinitesimals are somehow more intuitive to grasp than epsilon-delta ...
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Was the early calculus inconsistent?

This question does NOT concern the RIGOR, or lack thereof, of the early calculus. Rather the question is of its CONSISTENCY. George Berkeley wrote in 1734 with reference to the early calculus that ...
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Would Euler's proofs get published in a modern math Journal, especially considering his treatment of the Infinite?

I was wondering how mathematicians of today would treat, for example, Euler's proof of zeta(2). In William Dunham's book 'Journey through Genius' ( ...
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Non standard Algebraic Topology

Let *$\mathbb R$ a field of non-standard real numbers (or any real closed field) equipped with its natural generalized metric $d(x,y)=|x-y|$. Equip *$\mathbb R^2$ and *$\mathbb R^3$ with the ...
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Defining the slowest divergent series

This question might seem too fuzzy, and if so, I will be happy to withdraw it. Until then, here it is: I know that a method of slowing a divergent series of positive reals is to replace the $n$-th ...