This is rather neat: an ultrafinitist is one who denies the existence of infinite sets, in particular, the set N of natural numbers. The reason being that N can never be completed.
A lot of serious work on ultrafinitism was accomplished by Esenin-Volpin in the 1960’s.
Similarly, finitism is where you believe an object does not exist unless it can be constructed from N in a finite number of steps. In the book “Philosophy of Set Theory”, those who allow countably infinite objects are classified as classical finitists, and those who deny even countably infinite objects are classified as strict finitists.
Finitism is much older than ultrafinitism and dates back before Aristotle. For more information, check out wikipedia. Anyways, here’s a joke I created just for you guys!