1. 0 is a number.
2. The immediate successor of a number is also a number.
3. 0 is not the immediate successor of any number.
4. No two numbers have the same immediate successor.
5. Any property belonging to 0 and to the immediate successor of any number that also has that property belongs to all numbers.


As expressed in Galileo's Finger: The Ten Great Ideas of Science (2003) by Peter Atkins, Ch. 10 "Arithmetic : The Limits of Reason", p. 333 - Peano axioms

Giuseppe Peano Quotes

1. 0 is a number. 2. The immediate successor of a number is also a number. 3. 0 is not the immediate successor of any number. 4. No two numbers have...

1. 0 is a number. 2. The immediate successor of a number is also a number. 3. 0 is not the immediate successor of any number. 4. No two numbers have...

1. 0 is a number. 2. The immediate successor of a number is also a number. 3. 0 is not the immediate successor of any number. 4. No two numbers have...

1. 0 is a number. 2. The immediate successor of a number is also a number. 3. 0 is not the immediate successor of any number. 4. No two numbers have...