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Finding a basis of an infinite-dimensional vector space? 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, some of which, again, have easily describable bases
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infinity - What is the definition of an infinite sequence . . . Except for $0$ every element in this sequence has both a next and previous element However, we have an infinite amount of elements between $0$ and $\omega$, which makes it different from a classical infinite sequence So what exactly makes an infinite sequence an infinite sequence? Are the examples I gave even infinite sequences?
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Understanding the determinant of an infinite matrix It seems natural that the infinite matrix should also have determinant equal to $1$ but I don't see how the above formula gets this What about a triangular matrix with diagonal elements equal to $1$?
One divided by Infinity? - Mathematics Stack Exchange 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 who find it very difficult to accept the manipulation of infinite quantities in any way