It’s difficult to explain (in a sense of telling rather than teaching) advanced math to children or even some adults. However if you are really good at Maths you almost always can find a way. The problem is I’m not. That’s why I am asking if you can give me some elegant and simple examples from any part/field of math like mine written below (obviously I’m not the author, just heard it somewhere)
Th. Let G and H be groups, and let φ: G → H be a homomorphism. Then then image of φ is isomorphic to the quotient group G / ker(φ).
“Explanation to a 10 years old”. the CEO of a company doesn’t need to lead all employees; he just can give orders only to the heads of departments.
Today I took the day off of work to have a little alone time with my FR-S. I decided to tackle some simple maintenance and one of the things that entailed was the differential fluid. Everything went smoothly, but the magnetic drain bolt had some magnetic gunk (supposedly normal). I brought it inside and cleaned the black gunk off with paper towels and discarded them in the trash. I cleaned up some left over fluid that dribbled on the differential and tossed it in the trash too.
Our trash is right next to the closet that has our gas furnace and water heater. Later today day my girlfriend came home and said it smelled like natural gas and freaked out and called the emergency gas line thinking we had a leak. (It’s starting to get cold here so our heat is on) I thought it smelled familiar but agreed we should have it checked out. The gas guy came and got no readings of gas but smelled the odd smell…
… the smell was the NASTY DIFF FLUID IN MY TRASH CAN! I was super embarrassed when I found out and I’m not sure if I want to release this confession to my girlfriend… I took out the trash shortly after.
TLDR: I thought my horrible smelling differential fluid in my trash can was a natural gas leak and called emergency gas services
I already am subbed to Everyday Driver as well as TST. Just want to listen to something different, but Matt’s show is the only car podcast I know that is isn’t so “corporate” and has interviews with people in and around the industry. One of Matt’s finest moments was challenging the Forza’s employee and their e sports model. I want another podcast on my list that’d be willing to do that!
Thanks for your help!
I’ve seen a bit on Quaternions and Octonions and how they lose the commutative and associative properties, but it is implied that the difference in the answer is purely a change in sign. Is that truly the case?
I’m particularly curious about this as I’m making my own system of mathematics and one key difference is that in my system, sign is purely context and handled separately from calculating magnitude.