What are...p-adic integers?

Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What are...p-adic integers? Or: Climbing infinite trees.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

Thumbnail picture and other pictures.
https://www.quantamagazine.org/how-th...

Material used.
https://math.uchicago.edu/~tghyde/Hyd...
http://www.madore.org/~david/math/pad...
https://en.wikipedia.org/wiki/P-adic_...
https://blogs.scientificamerican.com/...
https://mathworld.wolfram.com/p-adicN...
https://math.mit.edu/classes/18.782/L...

Local-global.
https://en.wikipedia.org/wiki/Hasse_p...
https://en.wikipedia.org/wiki/Hasse%E...

More cool ways to think about p-adics.
   • What does it feel like to invent math?  
https://www.quantamagazine.org/how-th...
https://blogs.scientificamerican.com/...

Newton p-adic.
https://en.wikipedia.org/wiki/Hensel%...
https://math.stackexchange.com/questi...
https://math.stackexchange.com/questi...
https://mathoverflow.net/questions/85...

Creating trees in tikz.
https://ctan.math.washington.edu/tex-...

Mathematica.
https://demonstrations.wolfram.com/Ne...
https://demonstrations.wolfram.com/Ro...
https://demonstrations.wolfram.com/PA...
https://mathworld.wolfram.com/p-adicN...
https://library.wolfram.com/infocente...