How is the $\Rightarrow \Leftarrow$ symbol actually used in practice? I think my issue here is that I don't know what the symbol is meant to mean. For example, I know that $\implies$ means "which implies", and $\iff$ means "if and only if" or "iff". What does $\Rightarrow \Leftarrow$ mean? I'm thinking either "a contradiction" or "which implies a contradiction".
2026-05-15 21:37:05.1778881025
Implementing the $\Rightarrow \Leftarrow$ contradiction symbol?
1.1k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
The symbol means nothing more and nothing less than a casual declaration that a contradiction has been reached in an argument/proof. It has no inherent meaning, logically. I've see some use it in classrooms, writing it precisely following the point at which a contradiction has been revealed, as a sort of shorthand.
To be honest, the use of arrows, as in$\Rightarrow \Leftarrow$, is an abuse of notation, in the sense that it has nothing to do with implication, nor reverse implication. I think you're trying to read more into the expression, which is not standard, but rather, shorthand, as suggested in my first paragraph.