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.

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 …

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.

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 …

Jan 31, 2025 · There are the following textbooks to learn about infinite-dimensional manifolds: "The Convenient Setting of Global Analysis" by Andreas Kriegl and Peter W. Michor

Nov 28, 2018 · I am in need of examples of infinite groups such that all their respective elements are of finite order.

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.

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 ...

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 …

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