In intuitionist logic, a proof of (A or B) means a proof of A, or a proof of B, whereas in Classical logic, a proof of (A or B) may be done withouth either proving A or proving B.
I'm trying to get an example ( preferably simple, because i'm really beginner in mathematics ) where we can prove (A or B), withouth either proving A or B.
Someone told me that considering Riemann Hypothesis as RH, we can prove RH or ~RH withouth either proving RH or ~RH . But riemann Hypothesis is too advanced for me.
Can anyone provide me a simpler example of a proof of A or B that doesnt prove A, and also doesnt prove B ?
Is this kind of proof will always be a proof by contradiction ( proving that ~A and ~B derives a contradiction ) ? Is that why intuitionistic logic rejects proof by contradiction ?
Thanks a lot