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What is infinity divided by infinity? - Mathematics Stack Exchange 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
Examples of Infinite Simple Groups - Mathematics Stack Exchange Richard Thompson's groups $T$ and $V$ are well-known examples of infinite simple groups See this answer of mine for more details, or look up the article Introductory notes on Richard Thompson's groups by Cannon, Floyd and Parry
Infinite-dimensional manifolds: Fréchet, Banach and Hilbert manifolds . . . 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 types of manifolds of infinite dimension: Fréchet manifold Hilbert manifold Banach manifold ILH manifold
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 $1$?
How is an infinite direct sum defined? - Mathematics Stack Exchange 2 I am reading about infinite direct sums and I just need some clarification To say that a finite sum of say modules is direct we want to show that the intersection of all those finite modules is 0 Is the definition analogous for infinite direct sums? As in an infinite sum of modules is direct iff the infinite intersection of all the modules
Fubinis Theorem for Infinite series - Mathematics Stack Exchange In the book that I've read, there is one point where the author suggest to begin the proof of the Fubini's Theorem for infinite sum in the case when is non-negative after this try to generalize Bu