Abstract algebra-real numbers

Reference no: EM13117483

1. How can we picture real numbers "mod 2 pi" as something that goes round in a ring? How is that related to trigonometry?

2. Can we make a function from "real numbers mod 2 pi" to the rotations around the origin of the Cartesian plan so that this function is an isomorphism? Use the "natural" group operations on each set. Are these two groups communicative?

3. Can we make a function from the rotation matrices to the real numbers mod 2 pi to make an isomorphism? How? Is there a problem regarding commutativity here?

Reference no: EM13117483

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