We have all been there, when a formula works for the first 30 parameters, but it is not sufficient for a proof. My question is where one can actually just check a finite number of cases, to conclude ...
The Completeness Theorem in first-order logic states that any mathematical validity is derivable from axioms. Hence, any informal mathematical proof (which is rigorous) can be translated into a formal ...
I've just been asked for a good example of a situation in maths where using infinity can greatly shorten an argument. The person who wants the example wants it as part of a presentation to the general ...