What is the Axiom of Infinity? (Set Theory)

An explanation of the Axiom of Infinity in Set Theory, which will take our universe from a basic universe to a Zermelo Universe.
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Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy, The Oxford Companion to Philosophy, The Routledge Encyclopedia of Philosophy, The Collier-MacMillan Encyclopedia of Philosophy, the Dictionary of Continental Philosophy, and more! (#settheory #Peano)

[@InventiveHarvest]

1) each natural number is a set (von Neumann)
2) unions of sets are sets (Russell)
.: the set of all nats is a set
QED

[@HUEHUEUHEPony]

You assume infinite unions so you need infinity to do 2

[@InventiveHarvest]

@@HUEHUEUHEPony I can use mathematical induction as introduced in the previous video.

[@assiakessai]

Thanks alot of explaining the infinity ♾️ axiom could you please speak about the axiom of equality

[@deed18]

Reading cantor in math rn

[@JonSebastianF]

Noooo, no explanation of the definition of a natural number, on the last slide? :'(

[@InventiveHarvest]

The natural numbers were defined by von Neumann in this series
czcams.com/video/MZOA2ET0FtI/video.htmlsi=rT63cli255DfUlff

[@scoon2117]

Infinity is greedy