0u = 0 PROOF: A short play
Are 0u and 0 just the same? Watch this mini drama brought to you by Derby Maths Society and Professor Peter Larcombe to find out. We also had a bit of help from OpenAI!
A reminder of the 10 axioms listed below. Also recommended is the 10 axioms video also on this channel.
The story was devised by Derby Maths Society (Natalie.)
OpenAI created the play structure.
Jasper.ai was used for the haunting image of the mathematical lovebirds.
Ten Axioms of vector spaces
1. The sum of u and v, denoted by u + v, is in V
2. u + v = v + u
3. (u + v) + w = u + (v + w)
4. There is a zero vector 0 such that u + 0 = 0
5. For each u in V, there is a vector -u in V such that u + (-u) = 0
6. The scalar multiple of u by c, denoted by cu, in V
7. c(u + v) = cu + cv
8. (c + d)u = cu + du
9. c(du) = (cd)u
10. 1u = u