# Natural Numbers

1. Jan 6, 2009

### snits

Why do some people define the natural numbers as the integers 0,1,2,3... while others define them as the integers 1,2,3... ?

2. Jan 6, 2009

### HallsofIvy

Staff Emeritus
The former, 0, 1, 2, ..., (now usually referred to as the "whole numbers"), historically, was used by Peano when he set up "Peano's axioms" for the natural numbers. Modern treatments usually start with 1, 2, 3, ... It really doesn't matter which you use as long as you are consistent.

3. Jan 6, 2009

### Hurkyl

Staff Emeritus
I don't remember the last time I've seen a modern treatment starting with 1 instead of 0!

4. Jan 6, 2009

### CRGreathouse

Ditto. I thought it was the reverse: 1, 2, 3, ... was classic for the Peano axioms, but modern treatments use 0, 1, 2, ....

5. Jan 6, 2009

### HallsofIvy

Staff Emeritus
Oh, dear,am I living backwards?

6. Jan 6, 2009

### Werg22

Edmund Landau's famous Foundations of Analysis starts with 1. 0 is then defined as an equivalence class.

7. Jan 7, 2009