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Peano axioms 
Context: 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.
                                    
 
                             
                             
                             
                             
                             
                             
                            