We use integers so much in math that it never occurred to me before yesterday that this is a weird word with a weirder symbol associated to it. Wikipedia explains this very nicely.

The words integer and entire share the same Latin root: in (“not”) plus tangere (“to touch”). Google says that the first known use of the word integer was in 1571 by Thomas Digges in a book called A Geometrical Practise Named Pantometria. The word origin still doesn’t make complete sense to me but then I don’t know any Latin. The symbol $\mathbb{Z}$ comes from Zahlen, which is German for numbers, and was first used by Hilbert.