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definition - Is infinity a number? - Mathematics Stack Exchange 4 Infinity is not a number, but some things that can reasonably be called numbers are infinite This includes cardinal and ordinal numbers of set theory and infinite non-standard real numbers, and various other things There are various different things called infinity
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
elementary set theory - What is the definition for an infinite set . . . However, while Dedekind-infinite implies your notion even without the Axiom of Choice, your definition does not imply Dedekind-infinite if we do not have the Axiom of Choice at hand: your definition is what is called a "weakly Dedekind-infinite set", and it sits somewhere between Dedekind-infinite and finite; that is, if a set is Dedekind
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