I don't need to prove a stronger claim. Equality requires showing that all cases are the same. He is the one who asked if they were always the same. In other wo

I don't need to prove a stronger claim. Equality requires showing that all cases are the same. He is the one who asked if they were always the same. In other words, if they were equal. Inequality doesn't require that all cases are shown to be the same. It only requires that there is a single difference. Consider that 110 is different to 111 despite the fact that they both share a common prefix. If you're correct and I must prove that 11 and 11 are not equal to each other in order for these numbers to be different then it must be the case that 1 != 1 for the very concept of differences to exist. If that is true then the entire of mathematics breaks down because the identity function no longer holds.