a kernel of lie theory


just like how infinitesimals are useful because they're indiscernible from 0, but have the advantage of being able to be divided by.

the other important number besides 0 is 1. gpt even suggested it as i was typing it.

the monad of 1 is numbers of the form (1 + ε) where ε is an infinitesimal. multiplying by them should be almost as good as multiplying by 1, aka a freebie.

this is just the lie algebra, and is why elements of it are always invertible. by using the infinitesimal version of a clifford algebra on the tangent space, we can use its rotor represention to see how the exponential map gives lie's third theorem.

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