<P> In mathematics , a proof is an inferential argument for a mathematical statement . In the argument , other previously established statements , such as theorems , can be used . In principle , a proof can be traced back to self - evident or assumed statements , known as axioms , along with accepted rules of inference . Axioms may be treated as conditions that must be met before the statement applies . Proofs are examples of exhaustive deductive reasoning or inductive reasoning and are distinguished from empirical arguments or non-exhaustive inductive reasoning ( or `` reasonable expectation '' ) . A proof must demonstrate that a statement is always true ( occasionally by listing all possible cases and showing that it holds in each ) , rather than enumerate many confirmatory cases . An unproved proposition that is believed to be true is known as a conjecture . </P>
<P> In mathematics , a proof is an inferential argument for a mathematical statement . In the argument , other previously established statements , such as theorems , can be used . In principle , a proof can be traced back to self - evident or assumed statements , known as axioms , along with accepted rules of inference . Axioms may be treated as conditions that must be met before the statement applies . Proofs are examples of exhaustive deductive reasoning or inductive reasoning and are distinguished from empirical arguments or non-exhaustive inductive reasoning ( or `` reasonable expectation '' ) . A proof must demonstrate that a statement is always true ( occasionally by listing all possible cases and showing that it holds in each ) , rather than enumerate many confirmatory cases . An unproved proposition that is believed to be true is known as a conjecture . </P>
what do we call statements that we assume to be true without proofs
what do we call statements that we assume to be true without proofs
axioms
axioms