Aug 11, 2012 · I know that $\\infty/\\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as …

The other day, my teacher was talking infinite-dimensional vector spaces and complications that arise when trying to find a basis for those. He mentioned that it's been proven that some (or …

Nov 5, 2015 · My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of …

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 Geometric Series Formula Derivation Ask Question Asked 12 years, 2 months ago Modified 4 years, 5 months ago

A set A A is infinite, if it is not finite. The term countable is somewhat ambiguous. (1) I would say that countable and countably infinite are the same. That is, a set A A is countable (countably …

The dual space of an infinite-dimensional vector space is always strictly larger than the original space, so no to both questions. This was discussed on MO but I can't find the thread.

Dec 25, 2015 · Extending to the infinite case, we can show that, when we distribute out the product for S S, we get the sum of n 1 n over all integers writable as a product of primes - …

Jan 11, 2016 · 29 Well, there are a few notions of "infinite" sets that aren't equivalent in ZF. Z F One sort is called Dedekind-infinite ("D-infinite", for short) which is a set with a countably …

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 ∞ ∞ or infinite cardinals …