Axiom of infinity?

[CRGreathouse]

Main Question or Discussion Point

In ZF, the axiom of infinity says that the set of natural numbers exists. I was wondering if there was a (finitist?) weakening of ZF that included the axiom "the class of natural numbers exists".

 

[CRGreathouse]

Wait, this is a dumb question, isn't it. This actually follows from a suitable definition of classes and ZF - the axiom of infinity.

Sorry.