'To Infinity and Beyond': What is Transfinite Induction?

"To Infinity and Beyond" may feel a bit childish mathematically, well, that is until you learn more about ordinals and different sizes of infinity. One way this comes up in proofs is with Transfinite induction arguments. So, what is Transfinite Induction? Here we introduce the topic and go through a transfinite induction proof of something that, although there is a much simpler solution, generalizes the possibilities for a set that satisfies the conditions.

My Kofi Page:
_____________________
_____________________

WHAT GEAR I USED FOR THIS VIDEO:

DISCLAIMER: Links included in this description may be affiliate links. If you purchase a product or service with the links that I include here, I may receive a small commission. There is no additional charge to you! Thank you for supporting my channel and for helping me create these free videos!

[soneriftar]

and this video is the proof of necessity of an introduction for complex subjects😉

[NikolajKuntner]

Editing is painful, not just because of the work but also the waiting time and file size. Finite but significant file size on my laptop. The n'th Neumann ordinal has n members, I'd say that's a convenient way to double-check. Now as per the example a month ago, assuming N to be well-ordered leads to existence claims that cannot be realized - but another definition that's in itself more harmless is as follows: An ordinal is a transitive set of transitive sets. Feels like "A" is a bold symbol choice for the union of lines in 16:12, or I misunderstood something.

[davidwright]

That set had three elements, representing the integers 0, 1, 2. So 'second' (2 as an ordinal) is the third element in the set. If I understand it right.

[NoNTrvaL]

Thanks for making a video based on my profile pic 😂👍

[numericalcode]

2, 3 whatever. Who can tell the difference?

[glendon]

Why do so many really smart people talk so ludicrously with their hands?

[psIII]

dude, you gotta write bigger and more clearly.