What is infinity divided by infinity? - Mathematics Stack Exchange
2012年8月11日 · 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.
What is the difference between "infinite" and "transfinite"?
2020年6月6日 · The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about $\infty$ or infinite cardinals somehow, which may be giving the wrong impression. But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes ...
calculus - Infinite Geometric Series Formula Derivation
Infinite Geometric Series Formula Derivation. Ask Question Asked 11 years, 7 months ago. Modified 3 years ...
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 ...
2021年3月5日 · 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
If $S$ is an infinite $\\sigma$ algebra on $X$ then $S$ is not …
Once you have a infinite collection of pairwise disjoint sets one can identify each of these as distinct elements where unions of sets are also distinct. So by taking all countable unions on this collection one would generate a set with uncountably many elements as …
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 ...
Finding a basis of an infinite-dimensional vector space?
2019年2月9日 · For many infinite-dimensional vector spaces of interest we don't care about describing a basis anyway; they often come with a topology and we can therefore get a lot out of studying dense subspaces, some of which, again, have easily describable bases.
What is the square root of infinity and what is infinity^2?
2016年11月13日 · An example of an infinite number in ${}^\ast \mathbb R$ is represented by the sequence $1,2,3,\ldots$. One way of constructing MAX is to use a finitely additive measure $\xi$ on subsets of $\mathbb{N}$ with values $0$ or $1$.
Infinite group has infinitely many subgroups, namely cyclic …
2017年12月1日 · I think the contrapositive is much clearer: If a group has finitely many subgroups, then the group is finite. ...