N and Order | Axiomatic Set Theory, Section 3.2

We prove the natural ordering on the natural numbers is a total order.

Transitivity (0:00)
Asymmetry (6:02)
All elements are comparable (8:45)

[davidwhyman]

these videos came in handy while revising for my set theory exam, many thanks

[johnrobin]

I like how, though there is a time gap between these videos, you have me digging through my notes, i.e. the two lemmas from part 3.1 and how they came into play during the comparability proof. I liked that induction "inception" idea, as it made me appreciate how induction can be used with sophistication. It's especially interesting to see how false antecedents in induction break outside the typical "show this is true" argument, i.e. how we can get as much usefulness out of an induction proof if P(x) is false and that is carried through.

[teok]

i'll watch all your videos when i am done with real analysis, topology and measure theory which i am taking this semester, although i am studying physics, and maybe one day i'll cite you