elementary set theory - What do finite, infinite, countable, not ...
What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago
linear algebra - What, exactly, does it take to make an infinite ...
Oct 31, 2017 · Hence a vector space is infinite dimensional iff it has a basis which is infinite. If your infinite dimensional space has an inner product and is complete with respect to the …
general topology - Why is the infinite sphere contractible ...
Why is the infinite sphere contractible? I know a proof from Hatcher p. 88, but I don't understand how this is possible. I really understand the statement and the proof, but in my imagination this...
How can I define $e^x$ as the value of infinite series?
Are you familiar with Taylor series? Series solutions of differential equations at regular points? From what foundation/background are you approaching this problem?
One divided by Infinity? - Mathematics Stack Exchange
Infinite decimals are introduced very loosely in secondary education and the subtleties are not always fully grasped until arriving at university. By the way, there is a group of very strict …
Infinite class of closed sets whose union is not closed
Aug 4, 2016 · 0 Since singletons in R are closed in usual topology. We can think about infinite class of singletons {x} where x belongs to (0,1] then there union will be (0,1] which is not …
In an infinite sum, is there an actual term at an infinite position?
Nov 18, 2023 · As for what infinite summation means ... Zeno's first paradox maps to this very problem. Infinite summation shows how an infinite number of terms can sometimes add up to …
What is the difference between "infinite" and "transfinite"?
Jun 6, 2020 · 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 …
Union of infinite sets and infinity - Mathematics Stack Exchange
May 24, 2019 · 0 Nothing new happens in the case of infinite unions. An element belongs to the union of a family of sets if and only if it belongs to at least one of them.
How can Cyclic groups be infinite - Mathematics Stack Exchange
Oct 4, 2020 · I am a little confused about how a cyclic group can be infinite. To provide an example, look at $\\langle 1\\rangle$ under the binary operation of addition. You can never …