Ordinary mathematics
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In the philosophy of mathematics, ordinary mathematics is an inexact term, used to distinguish the body of most mathematical work from that of, for example, constructivist, intuitionist, or finitist mathematics.
Ordinary mathematics is usually studied within the universe SN, or sometimes Vω+ω (see Von Neumann universe). Contrast with finitist mathematics, which limits to the study of Vω (see hereditarily finite sets), or with metamathematics and the study of large cardinals, which study objects contained in a larger universe.
Ordinary mathematicians generally assume the axiom of choice (at least, because it makes their work easier), whereas constructivists reject it on the grounds that it is "non-constructive", and also reject the law of excluded middle, which can be derived from it.
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