StarkNet's Cairo Language: the Felt Integer Type Explained

In this video I explain how computers represent and do arithmetic on numbers, and some of the problems there. Then we look at sets, groups, rings, and finite fields, and see how these tools can provide a more robust way to do arithmetic over integers. Finally I talk about how these ideas are used in StarkNet's Cairo language to implement their "felt" (field element) integer type, and we go over some code examples.

Twitter:   / jordanmmck  

0:00 - Intro
0:25 - Video Overview
1:00 - Numbers & Arithmetic in Computers
1:23 - Bits
2:37 - Information Theory
5:34 - CPU Architecture
7:41 - INTS, UINTS, FLOATS
14:54 - Arithmetic
20:45 - Problems with Division
30:16 - Sets, Groups, Rings, Finite Fields
30:52 - Sets
32:44 - Groups
38:26 - Rings
40:58 - Finite Fields
44:03 - Prime Order Fields
47:14 - Discrete Log Problem
48:20 - Cairo FELTs
50:49 - Cairo Code Examples
57:42 - Outro