Different coordinate systems can map different numbers to different points without changing any features of the resulting geometric object — Pfhorrest
You probably need to qualify this. Take the circle x^2+y^2=1 in the standard Euclidean plane and lengthen the scale on the x-axis, so that the circle becomes an ellipse. That's a "different coordinate system". — jgill
I wish I had this site when I was at school, because I suspect that, with the right wording, you could make fdrake do a lot of your homework. — Kenosha Kid
Yeah fdrake is awesome and I would love to see him continue what he was doing in this thread; or for someone else to take over where he left off. — Pfhorrest
I wish I had this site when I was at school, because I suspect that, with the right wording, you could make fdrake do a lot of your homework. — Kenosha Kid
Interesting thread. Ambitious too. — Kenosha Kid
Yeah fdrake is awesome and I would love to see him continue what he was doing in this thread; or for someone else to take over where he left off. — Pfhorrest
I can do some more of the basic axiomatic maths, but I've been cheating and looking ahead at axiomatic QFT and decided that I really need to study more mathematics. I don't know C*-algebra from a 32C-wonderbra — Kenosha Kid
Would that be sufficient? — Kenosha Kid
I know how to get from simple fields to wavefunctions and from densities to wavefunctions uniquely -- that's simple enough. — Kenosha Kid
What’s going on in that black box, stepping up through sets, numbers, spaces, differentiable manifolds, Lie groups, quantum fields, particles, chemicals, cells, organisms, etc. — Pfhorrest
So you'd need linear operators on vector spaces, differentiation+integration, complex numbers... If I gave you definitions of those things, would you be able to to do what you needed to do with them? Can you do the thing where you go from linear operators on vector spaces to linear operators on modules if required?
The vector space construction needs mathematical fields (commutative rings with multiplicative inverses), which needs groups. — fdrake
I guess a good aim atm is continuum mathematics. — Kenosha Kid
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