Why and how are paradoxical statements expressed mathematically?

Question

Why and how are paradoxical statements expressed mathematically?

In: Mathematics

Answer 1

Paradoxical statements are frequently used when trying to prove that some mathematical fact must be true. In order to prove something must be true mathematicians assume the opposite is true. If the opposite of what you want to prove somehow leads to a paradox that means logically the thing you tried to prove must be true. This kind of proof is called a proof by contradiction.

Basically if you show that the opposite of what you believe leads to paradoxes the thing you want to show is true must be true.