I’m talking about the set {…, -2, -1, 0, 1, 2, …}. The set R (reals) and N (naturals) have obvious names. Why was the letter Z chosen? I have heard it is something in german, but I’m not sure. Perhaps it’s arbitrary.

It’s from the German word *Zahl*, a number ( plural *Zahlen*).

Who first “coined” Z for the integers? Must have been a German mathematician. Gauss?

Edmund Landau ( 1877 - 1938) used fraktur Z with a bar over the top for the integers. The use of Z is apparently due to Bourbaki who was ( were) mainly French.

Err . . . why do I think they’re called “J”? I can certainly remember in any number of proofs/problems writing something to the effect of “n [element sign/loopy E] J”.

And they passed me. Act of charity, regional difference, or what?

I, too, have seen the set of integers called “J”. And apparently, mathematicians have seen it both ways.

Well, one thing you have to remember is that mathematicians are free to call anything anything. For example, we (I) regularly use pi for all sorts of things different from the ratio of the circumference to the diameter of a circle. And if someone wants to call the integers I or J or Sam, they will do it. I think that the book by Birkhoff & Mac Lane that introduced so many of us to modern algebra used J. People do use I all the time too. Incidentally, H (for Hamilton) is usually used for the quaternions since Q (for quotient, I assume) is used for the rationals since R is used for the reals.

Notice that this is very different from the chemists who have nomenclature meetings and then the journals enforce those decisions. Mathematicians are an unruly bunch.