However, we also accept many statements without bothering to prove them But, in mathematics we only accept a statement as true or false (except for some axioms)
Saying A =? B indicates that whenever A is accepted, then we also must accept B The important point is that the direction of the implication should not be
3 oct 2016 · The remedy in such situations is simple: do not choose Proof of Theorem 1 4 without choice Consider the family of all open balls B(x, ?) where
A statement that is true but not as significant is sometimes called a proposition A lemma is a theorem whose main purpose is to help prove another theorem A
If you don't accept a rule, this is not chess any more The only kind of debates is to whether the theory is math- ematically fruitful or interesting 2 4
A definition in mathematics is the laying down of the mathematical meaning of to be accepted without proof (and even without certainty); but an axiom is
not qualify as such, since it is justified by mathematical proofs that do not mathematical proposition accepted without proof in the various branches of
cal practice (see p 38) Thus, proof is considered to be a tool, not only for acceptance/generation of new mathematical knowledge but for all the other
19 mai 2019 · disciple: I would say that we do not just pretend that sets exists, but anyway: Yes, as I said, formal proofs are also mathematical