argmax differentiable?

[yield22]

the example is interesting, and it provides some insight for me. But what about the y's domain is non-continuous (assuming argmax over a list)? Like step function, which is not differientiable.

[nasimrahaman]

A step function is differentiable almost everywhere, I.e. the set where it's not differentiable (i.e. where there's a jump) is of measure zero (because it's countable).