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How to prove the infinite number of sides in a circle? 0 There is a way of proving that there is "infinite number of sides in a circle", in the following sense Infinity was a number to both Kepler and Leibniz who spoke of a circle as an infinite-sided polygon This point of view is useful in analyzing the properties of the circle, as well as more general curves, in infinitesimal calculus
linear algebra - Is there a quick proof as to why the vector space of . . . 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 space is finite dimensional, then it is a countable set; but there are infinite-dimensional vector spaces over $\mathbb {Q}$ that are countable as sets
Does infinite equal infinite? - Mathematics Stack Exchange All three integrals are divergent and infinite and have the regularized value zero, but two of them are equal but not equal to the third one In other cases of divergent integrals or series, the regularized value and or growth rate (germ at infinity) or behavior at a singularity can differ as well or the differences can compensate for each
Subspaces of an infinite dimensional vector space It is well known that all the subspaces of a finite dimensional vector space are finite dimensional But it is not true in the case of infinite dimensional vector spaces For example in the vector