Introduction to p-adic Numbers
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when asking about or explaining how to visualize the p-adics and their open balls with a concrete picture.
Recommended by 2 people across 2 different months, 2017 to 2019.
What it is
A roughly 17-minute introductory lecture on p-adic numbers, uploaded by Rokker815 in 2011. It covers the p-adic metric and builds a tree-like picture of the p-adic integers, including how open balls look.
What people said
Recommends esmo · 2017-04 · Mathematics Stack Exchange · on “Interpretation of open balls with the p- adic metric”
I got it from this YouTube video: [this video] At time 15:43, you can see the picture. This guy is also explaining why there is vertex on the left bottom. Unfortunately I still do not get him. @RobArthan
Recommends Viktor Vaughn · 2017-09 · Mathematics Stack Exchange · on “Visualizing $\textbf{Q}_p$ vs. $\textbf{F}_p((t))$?”
For visualizing the $p$-adics, here are some links: a MO post [LINK] , a picture [LINK] (see slide 28), and a video [this video] with a picture and some explanation.
Cites LoneStar · 2019-02 · Mathematics Stack Exchange · on “Open balls in $p$-adic numbers.”
I am new to $p$ -adic numbers and was watching an introductory video [this video] about it. At 14:51, he says that $r$ only takes values in the form of $p^n$ . However, I don't understand why $r$ must be restricted to numbers in the form of $p^n$ . Given any r that is not in the form of $p^n$ , there will be an integer $i$ such that $p^i<r<p^{i+1}$ . Thus, the open ball set of $r$ would be the same as $p^{i+1}$