[ionut_popa]

Not sure it's just notation but a mater of understanding.

In computer programming "exists" it's a matter of checking all the possibilities and find one, therefore is restricted to finite sets (and realistically speaking quite small the ones).

On the other hand in mathematics there is no such restriction. Existence is just an assumption, if there is at least one, then we go further with the assumption, no meter we talk about finite sets, infinite countable sets or infinite uncountable.

I'm working as a computer programmer for quite a long time and I also find this very annoying seeing people around thinking only finite when they have to solve real problems.