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According to Peano's axioms, in either system, it is the successor to the successor to the successor to the successor to the successor to 0.
It was the successor to the successor of the number 0.
It is the successor to 22. Its successor is 24.
They are both counting numbers and 5 is the successor of 4.They are both counting numbers and 5 is the successor of 4.They are both counting numbers and 5 is the successor of 4.They are both counting numbers and 5 is the successor of 4.
There is no highest integer because they go on for even. According to Peano's axiom for numbers, every integer N has a successor, N+1. The successor is larger than N. But the successor of the successor is even larger, and so on.