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Results tagged with nonstandard-analysis
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user 2000
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 that Abraham Robinson developed a theory of a hyperreal continuum that allows for a development of analysis procedurally akin to that of its founders.
3
votes
Am I doing a forcing argument here?
It looks like the "logic aspects" of the argument boil down to using compactness. [However, this appears to be moot since the argument may have flaws pointed out by Will Sawin.]
First, given a bound …
- 44.4k
6
votes
How is compactness related to countable saturation?
As Todd Trimble pointed out in the comments, the use of the term "compactness" in the Compactness Theorem does refer to the topological notion: the Stone space of the Lindenbaum algebra of a theory is …
- 44.4k
30
votes
Accepted
Which topological spaces admit a nonstandard metric?
The uniformity defined by a *R-valued metric is of a special kind.
Let $(n_i)_{i<\kappa}$ be a cofinal sequence of positive elements in *R. We may assume that $i < j$ implies that $n_i/n_j$ is infin …
- 44.4k