I would say that even though it may be commonly used it is a bad name for Integers because it is not mnemonic. "I" would be a much better name for the set of Integers I would think.

But whatever you call it should not be too much effort to state in the beginning of a presentation or chapter or book, these are the symbols we will be using:

I = Set of Integers, ....

Sure it might be redundant but it is also easy for the reader to step over such explanations if they are familiar with them, but come back if they find some symbol they are not quite sure of. Question is are we trying to make the book easy for readers to understand, or short for the writer to write.