Letters Used to Name Integers and Irrational Numbers

Date: 1/13/96 at 9:25:46
From: Barbara R Carpenter
Subject: integers

Dr. Math
My students wonder why the set on integers is referred to as J.  

i.e.  

J = {... -3, -2, -1. 0, 1, 2, 3, ...}

doesn't it make sense to refer to it as I?

And what letter is used to name the set of irrational numbers?

Thanks,

The Elementary Students at Suomi College

Date: 3/1/96 at 20:0:58
From: Doctor Jodi
Subject: Re: integers

Hi Barbara! 

I wondered why we called integers "j" for a long, long time 
when I was younger.  Mathematicians like use letters to refer 
to things.  And we seem to get used to using particular letters 
so that we remember what they stand for more quickly.  

Mathematicians use the letter i - for imaginary - to refer to the 
square root of negative one.

-Doctor Jodi,  The Math Forum

Date: 3/2/96 at 11:27:15
From: Doctor Ken
Subject: Re: integers

Hello!

If I were you, I'd be confused too!  I can't see any reason why 
the set of integers would be called J.

But actually, I've never seen it called J.  Most mathematicians 
(when they're talking to each other, anyway) use Z to refer to 
the set of integers.  The reason for that is the German word 
"zahlen" which means "to count."  And "Zahl" means "number."

The rational numbers are called Q, probably for "quotient."  
I don't think I've ever heard a name for the set of irrational 
numbers, but that's okay, people refer to them as R-Q (R is the 
set of real numbers).

-Doctor Ken,  The Math Forum