In
mathematics, a proof is a demonstration that, assuming certain
axioms, some statement is necessarily true. A proof is a
logical argument, not an
empirical one. That is, one must demonstrate that a proposition is true in all cases before it is considered a
theorem of mathematics. An unproven proposition for which there is some sort of empirical evidence is known as a
conjecture. In virtually all branches of mathematics, the assumed axioms are
ZFC (Zermelo–Fraenkel set theory, with the axiom of choice), unless indicated otherwise. ZFC formalizes mathematical intuition about
set theory, and set theory suffices to describe contemporary
algebra and
analysis.
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