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*What is the mathematical definition of "number"?*

It seems odd to me that one of the most commonly used mathematical objects has no clear definition. Should the definition of number be "a member of a mathematical structure"? The notion of "sturcture" isn't clearly defined, so I don't like it. Also it will include functions, vectors, tensors, etc.

Or should it be "a member of a magma [which includes group, rings, and fields] that can not be written as an n-tuple"? This will exclude complex numbers, which are isomorphic to R

^{2}.

Both of these will exclude cardinals and ordinals, which are not sets, let alone magmas.

IMHO, no definition of "number" can be given such that it encompasses all of the inclusions and the exclusions. Shouldn't we just expel this term from mathematical parlance and just talk about "elements of [put name of set/class/space/vector space/structure here]"?

ps. admins, you deleted the wrong thread

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