How XPath compare values in prediates

A user asked question similar to following, on IBM developerWorks XQuery and XPath forum:

What does A = B and A != B mean in XPath expressions?

Michael Kay provided a very nice explanation to this:
The operators "=" and "!=" in XPath use "implicit existential quantification". So A=B is shorthand for "some $a in A, $b in B satisfies $a eq $b" (the longhand form is legal in XPath 2.0), while A!=B is shorthand for "some $a in A, $b in B satisfies $a ne $b".

So, not(A=B) is true if there is no pair of items from A and B that are equal, while (A!=B) is true if there is a pair of values that are not equal. In practice, you nearly always want not(A=B).