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Attempting to create a generalized graph of mathematics


ALine
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ok, so I am taking discrete mathematics this semester and I have no idea what is going on. So imma get to understanding that first before even attempting this project that I have been procrastinating on.

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On 7/13/2020 at 5:20 AM, ALine said:

And what is symmetry from a mathematicians perspective?

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Weyl's definition of symmetry: “a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation.

 

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interesting, so for clarity and learning sake say if I have a 0 and I multiplied it by a 1 would the 0 be considered symmetrical? Because I started with a 0 and ended up with a 0?

Edited by ALine
added some words
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Well, the identity is not considered to be an interesting symmetry transformation, because everything is symmetric under it. It does play a role in the theories that involve symmetry (mostly in group theory as far as I know).

Example:

Consider three numbers, i, j, k. And a function alpha:

\[\alpha\left(i,j,k\right)=ij+jk+ki\]

And the transformation,

\[\pi\left(i\right)=j\]

\[\pi\left(j\right)=k\]

\[\pi\left(k\right)=i\]

Then we say alpha is symmetric under pi.

 

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  • 1 year later...

So it's been a minute and I was reminded of this by a fellow forum member reposting about it. How much progress have I made you might ask? Literally none, This problem is a fuuuuuuuuuuuudge ton more difficult than I originally imagined. I am going to keep try, but its gonna be a while.

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