3 ms·

What is true in mathematics is whatever leads to no logical contradictions.

• xyzzyz 15y ago
  There are cases when both a claim and its negation do not lead to contradiction, but them both being true obviously does.
  • qntm 15y ago
    Thus, mathematics unexpectedly turns into a Choose Your Own Adventure novel!
    • xyzzyz 15y ago
      It's an amusing way to put this, but yes, it's true. An example of such situation is the case of continuum hypothesis. Both it and its negation has been proven not to lead to contradiction, so while most mathematicians ignore it, effectively treating it as being true, many set and model theorists play with things like Martin's axiom, which makes sense only if continuum hypothesis is false.