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### Why Use Q and Z?

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Date: 09/12/2001 at 17:07:21
From: Jim Truelove
Subject: Q and Z

Dr. Math -

Why is the letter Q used for rational numbers and Z for integers?

Thanks,
Jim
```

```
Date: 09/12/2001 at 17:41:39
From: Doctor Paul
Subject: Re: Q and Z

Hi Jim -

Q is for quotient - which is how rational numbers are identified.

Z is for Zahlen - the German word for integers.

- Doctor Paul, The Math Forum
http://mathforum.org/dr.math/
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```
Date: 09/24/2001 at 01:32:48
From: Tevis Howard
Subject: The Integer Symbol... Z

Dr. Math,

What is the history/etymology of the math symbol for integers, Z?

Thanks for your help.
```

```
Date: 09/24/2001 at 09:16:41
From: Doctor Luis
Subject: Re: The Integer Symbol... Z

The German word for "number" is "Zahlen." Several German
mathematicians made contributions to Number Theory (or
Zahlentheorie in German), which is, roughly speaking, the
branch of mathematics concerning theorems about the integers.
They used the letter Z to denote the set of integral "numbers" in
their textbooks, so I guess the usage just stuck over time.
Leonhard Euler and Karl Gauss were two such mathematicians
who made several important contributions to the field of Number
Theory. Others come to mind, but I'm sure you can find an
interesting book on the history of mathematics where you can
read about  them :-)

Anyway, the origin of the symbol Z for the set of integers is that
simple.

- Doctor Luis, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Definitions
High School Number Theory
Middle School Definitions
Middle School Number Sense/About Numbers

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