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

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 make any negative …

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 …

Oct 28, 2014 · e as sum of an infinite series [duplicate] Ask Question Asked 11 years, 5 months ago Modified 11 years, 2 months ago

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.

In his book Analysis Vol. 1, author Terence Tao argues that while each natural number is finite, the set of natural numbers is infinite (though has not defined what infinite means yet). Using Peano...

Dec 15, 2025 · Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?

Sep 10, 2019 · Your further question in the comments, whether a vector space over $\mathbb {Q}$ is finite dimensional if and only if the set of vectors is countable, has a negative answer. If the vector …

Apr 13, 2016 · Questions But from here I don't know if I am right, how to conclude and solve the converse part to say that we have a non zero limit, and another thing Can someone provide explicit …

17 Grigory has already answered your particular question. However, I wanted to point out that your question "How do you prove that a group specified by a presentation is infinite?" has no good answer …