[Serious mode]
How to prove that 1≠2?

We have equality is transitive, we have 1's successor is 2, we have...
No theorem ever said that a successor cannot be equal to the number itself
No theorem ever said that two numbers with different looks cannot be equal
1.000... is equal to 0.999... for example
A number can have many ways of presenting...

ASSUMPTIONS: 2:=S(S(0)), 1:=S(0), where S(x) denotes the successor of x, where x is a natural number.

Question

[Serious mode]
How to prove that 1≠2?

We have equality is transitive, we have 1's successor is 2, we have...
No theorem ever said that a successor cannot be equal to the number itself
No theorem ever said that two numbers with different looks cannot be equal
1.000... is equal to 0.999... for example
A number can have many ways of presenting...

ASSUMPTIONS: 2:=S(S(0)), 1:=S(0), where S(x) denotes the successor of x, where x is a natural number.

dan815 · Answer

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