# What is the mathematical symbol for integers?

1. Sep 17, 2007

### l46kok

The mathematical symbol for real numbers is R, with another vertical line coming down on the left side of the R.

What is the mathematical symbol for integers? can anyone draw it?

2. Sep 18, 2007

### bob1182006

$$\mathbb{Z}$$
there's also $$\mathbb{Q}$$ for rational numbers

and plenty more I think wikipedia has a huge list of math symbols (Not, greater/less than, is a subset, for every, there exists a, etc....)

3. Sep 18, 2007

### robert Ihnot

You must have noticed that 'N' is frequently used, such as: 1+2++++n=n(n+1)/2, and the 'nth prime is commonly denoted as' $$p_n$$. And the $$\sum_{i=1,N}x_i$$ Also: "If N is an odd perfect number....""Expressing N as the difference of two integral squares."

Examples are very, very numerous, but don't explain why N is the first letter of Number, and I of Integer. (If I might hazard a guess, we have to remember that small i alone represents the square root of -1. This means we could not easily go from big I to small i and really mean the same thing, but we can do it with N.)

Last edited: Sep 18, 2007
4. Sep 18, 2007

### HallsofIvy

Staff Emeritus
'N' is commonly used for what? In the examples you give 'n' is commonly used to represent a single interger or, more commonly, natural number. 'N' is commonly used to represent the set of all "natural numbers": positive integers.

5. Sep 18, 2007

### mathwonk

do others believe Z stands for "zahlen"?

6. Sep 18, 2007

### mathwonk

do others believe Z stands for "zahlen"?

7. Sep 18, 2007

### CRGreathouse

Yes.

Yes.

8. Sep 18, 2007

### robert Ihnot

Halls of Ivy: 'N' is commonly used for what?

I am only giving what were exact examples I saw on the internet. Here is one:

There are a number of ways to approach finding prime factors of large
natural numbers. 13.....An old-fashioned way which is often effective is to express N as the difference of two squares, that is, to find x and y such that
N = x^2 - y^2 = (x - y)*(x + y). One way to do this is to start with
x being the integer just larger than sqrt(N), http://mathforum.org/library/drmath/view/65801.html

mathwonk: do others believe Z stands for "zahlen"?

I thought Landau did that. I remember using his number theory book. However, it is not always the case, may have to do with the publisher. However, here are some facts:

Edmund Landau (1877-1938) denoted the set of integers by a fraktur Z with a bar over it in Grundlagen der Analysis (1930, p. 64). He does not seem to introduce symbols for the sets of rationals, reals, or complex numbers.

Q for the set of rational numbers and Z for the set of integers are apparently due to N. Bourbaki. (N. Bourbaki was a group of mostly French mathematicians which began meeting in the 1930s, aiming to write a thorough unified account of all mathematics.) The letters stand for the German Quotient and Zahlen. These notations occur in Bourbaki's Algébre, Chapter 1. http://members.aol.com/jeff570/nth.html

So the real credit goes to a Frenchman(s), not a German?

Last edited: Sep 18, 2007
9. Jan 20, 2010

### cathalcummins

After searching long and hard I discovered that the "identity element" symbol may be inserted into a LaTeX document via the bbold package. However, loading this package conflicts with the amsmath/assymb package which I use to give me blackboard font Real numbers etc as above.

My question is: can one define bbold locally as opposed to the preample - since whichever package loaded takes priority and I'm doing an assignment where I use both \mathbb{R} (amsmath) and \mathbb{1} (bbold)?