Axiom of Infinity

If x is an element of S then the successor of x is also in this set:

A set S exists containing the empty set, $\varnothing$ and the following rule is true:

If t is an element of S then the successor of t will be an element of S. The one element we already have in our set generates a second element:

$S(\varnothing)$

The same “domino” action happens here that we saw in induction. The set therefore has an infinite number of elements.

${ \varnothing, S(\varnothing), S(S(\varnothing)), ... }$