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-big infinity, for

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 all natural numbers is

Dec 10, 2023 · Here's a proof by induction that the resistance of a finite version of this ladder with $\ n\ $ rungs is indeed homogeneous of degree $1$ in the variable $\ R\ .$ Taking the limit as $\ …

Jun 6, 2020 · Infinite simply means "not finite", both in the colloquial sense and in the technical sense (where we first define the term "finite"). There is no technical definition that I am aware of for …

Meaning of Infinite Union/Intersection of sets Ask Question Asked 8 years, 11 months ago Modified 4 years, 4 months ago

An infinite number? Kind of, because I can keep going around infinitely. However, I never actually give away that sweet. This is why people say that 1 / 0 "tends to" infinity - we can't really use infinity as a …

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, …

Apr 24, 2013 · What might be interesting to notice (although it might be a little too advanced, if this is your first course in topology) that the family of sets in your example is locally finite. Union of a locally …

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 Mathematicians …

The two are effectively equivalent but the second method views the infinite series as a sequence of partial sums, which is more amenable to proofs and is more rigorous.