Abstract:Much mathematical writing exists that is, explicitly or implicitly, based on set theory, often Zermelo-Fraenkel set theory (ZF) or one of its variants. In ZF, the domain of discourse contains only sets, and hence every mathematical object must be a set. Consequently, in ZF with the usual encoding of an ordered pair a, b , formulas like {a} ∈ a, b have truth values, and operations like P( a, b ) have results that are sets. Such 'accidental theorems' do not match how people think about the mathematics and also c… Show more
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