A = B ⇔ (∀x.x ∈ A ⇔ x ∈ B)
What does "∀x.x" mean?
This expression means: saying 2 sets are equal, is equivalent to saying they're the same set, right?
Thank you.
[Math] What does the dot symbol mean
logicnotation
logicnotation
A = B ⇔ (∀x.x ∈ A ⇔ x ∈ B)
What does "∀x.x" mean?
This expression means: saying 2 sets are equal, is equivalent to saying they're the same set, right?
Thank you.
Best Answer
It is a separator between $\forall x$ and the formula $x\in A\iff x\in B$. It means that the context of $x$ is fixed to be that of the quantified value throughout the rest of the formula.