Support us on Patreon: https://www.patreon.com/user?u=86649007
#logic #excluded_middle
I love it when different parts of mathematics are brought together into a single perspective. In this video, we take a fresh look at simple logical operators such as 'and', 'or', and implication. We extend these operators to numbers, and we interpret them in terms of ordering. Did you know that logical implication is really just "less than or equal to"?
Here are some links to Eric Hehner's ideas if you want to dig deeper:
http://www.cs.toronto.edu/~hehner/
Hehner's website at the university of Toronto.
http://www.cs.toronto.edu/~hehner/BAUA.pdf
Article for the Mathematical Intelligencer. Good introduction to Hehner's unified system of logic and algebra.
These are some resources that Eric Hehner himself suggested for you if you want to learn more:
http://www.cs.utoronto.ca/~hehner/UA.pdf
http://www.cs.utoronto.ca/~hehner/BAUAvideo.mp4
0:00 Introduction
0:40 Binary logic
4:55 Truth values are ordered
6:41 Extending logic to arithmetic
9:14 Differences between logic and arithmetic
10:22 Functions and variables
11:34 Sums and products
12:29 Logical quantifiers
14:00 Shorter notation
15:19 Bunches and sets
This video is published under a CC Attribution license
( https://creativecommons.org/licenses/by/4.0/ )