I quit Math when they started using musical notes.
https://en.wikipedia.org/wiki/Musical_isomorphism
>>8036955
Oh yeah, well I quite math when they started using infinite sets.
>>8036955
Those are flat and sharp signs, you cunt. They raise and lower pitches, antirespectively. It's a joke.
Actually the musical isomorphism makes a lot of sense.
Vectors have upper indices. 1-forms have lower indices.
The flat morphism lowers the upper indices to lower indices and makes a 1-form from a vector field... (by taking inner products with respect to the metric)
>>8036967
>antirespectively
Why would you choose to write this way?
>>8036972
I didn't feel lime going back and change things around. First though, best thought.
>>8036991
At least your attitude is consistent.
>>8037001
Damn skippy
>>8036955
>wonder what this is about
>lowering and raising indices
Huh, never heard that notation. The more you know.
>not giving up when your indigenous bundles start sleeping
>>8037015
Well its a bit more than that. They are maps between the tangent and cotangent bundles. Vector fields are sections of the tangent bundle and 1-forms are sections of the cotangent bundle.
So what you get out of this is a way to map a vector field to a 1-form or vice versa.
