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 …

Feb 20, 2019 · The user @Eevee Trainer provided a nice explanation on how we define infinite nested radical in terms of limit of finite nested radical which should be insensitive of the starting point.

Jul 15, 2022 · Essentially, it is sought that these manifolds with infinite dimension are homeomorphic, as these topological spaces, to vector spaces of infinite dimension, and this gives rise to the following …

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...

Feb 9, 2016 · An infinite sum of irrational numbers can be rational. PROOF: Let the set A be all the positive irrational numbers and the set B be the negative irrational numbers.

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

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 …

Write out a few terms of the series. You should see a pattern! But first consider the finite series: $$\sum\limits_ {n=1}^ {m}\left (\frac {1} {n}-\frac {1} {n+1 ...