Depending on what you mean by "infinity", sure:

If you take it to mean "The cardinality of an infinite set", "X + 1" to mean "The set X with one more element added to it", and "X = Y" to mean "X and Y have the same cardinality", then "X = X + 1" is entirely true.

Mathematics, like programming, is ultimately founded on definitions.

I don't think infinity equals infinity. Not in the general mathematical sense anyway.