Mathematical logic and foundations Definition

Successor function

Definition

Let $\mathbb{N}$ be the set of natural numbers. The successor function is the function $S \colon \mathbb{N} \to \mathbb{N}$ with $S(n) = n + 1$ for each $n$ in $\mathbb{N}$ . The number $S(n)$ is the successor of $n$ .

Remarks

In the Peano axioms, $S$ is a primitive function, and the axioms do not define it. Then $n + 1$ is a name for $S(n)$ , and $1$ is a name for $S(0)$ . For example, $S(0) = 1$ , $S(1) = 2$ and $S(S(2)) = 4$ .

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Natural numbers object
Peano axioms concept
Successor function definition

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Tag	`0832XVR512`
URI	`m2://0832XVR512`
Kind	definition
Writing	W0 stub
MSC	03F30
Defines	Successor function
Uses	Natural numbers, Peano axioms

Successor function

Definition

Remarks

Reading path

Where this leads

Further reading

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