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- calculus - What is infinity divided by infinity? - Mathematics Stack . . .
One advantage of approach (2) is that it allows one to discuss indeterminate forms in concrete fashion and distinguish several cases depending on the nature of numerator and denominator: infinitesimal, infinite, or appreciable finite, before discussing the technical notion of limit which tends to be confusing to beginners
- Uncountable vs Countable Infinity - Mathematics Stack Exchange
As far as I understand, the list of all natural numbers is countably infinite and the list of reals between 0 and 1 is uncountably infinite Cantor's diagonal proof shows how even a theoretically complete list of reals between 0 and 1 would not contain some numbers My friend understood the concept, but disagreed with the conclusion
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 1 month ago Modified 4 years
- Example of infinite field of characteristic $p\\neq 0$
On the other hand, if we had $\overline{\mathbb{F}_p}\subseteq\mathbb{F}_p(T)$, then we would have that there were some $\frac{f}{g}\in \mathbb{F}_p(T)$ such that $\frac{f}{g}\notin\mathbb{F}_p$ and $\frac{f}{g}\in\overline{\mathbb{F}_p}$ (because $\overline{\mathbb{F}_p}$ is infinite and $\mathbb{F}_p$ is finite), and they would have to be
- elementary set theory - What do finite, infinite, countable, not . . .
Clearly every finite set is countable, but also some infinite sets are countable Note that some places define countable as infinite and the above definition In such cases we say that finite sets are "at most countable"
- algebra precalculus - The Infinitely Nested Radicals Problem and . . .
In mathematics, a nested-radical is any expression where a radical (or root sign) is nested inside another radical, e g $\\sqrt{2 + \\sqrt{3}}$ By extension, an infinitely nested radical (aka, a
- Exterior algebra for infinite dimensional vector spaces
DeWitt just introduces the infinite exterior algebra through a countably infinite basis If I recall
- Basis for $l^{\\infty}$ - Mathematics Stack Exchange
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