Is there a mathematical notation to write that, in a multiset of elements S, at least two of those elements are different?

Question

I'm looking to write down formally that a multiset of elements contains at least two elements that differs in value. e.g., S1 = {1,1,1,1,1,1} and S2={1,1,1,1,0,1} S1 has all identical elements, S2 has at least two elements that differs in value.

Answer 1

You can write $\exists x \exists y (x\in S \wedge y \in S \wedge x \neq y)$. This works whether $S$ is a set, multiset, or tuple as discussed in the comments to your question.

Answer 2

I would suggest

$S$ contains at least two elements that differs in value.

Don't mistake the lack of formulas for a lack of mathematical formality.