Abstract Groups

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Last updated 8:27 PM on 9/21/26

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Addition groups (Z, Q, R)

Identity: 0

Inverse: -x

Vibe: infinite & abelian (commutative)

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Multiplication groups (Q^x, R^x under x)

Identity: 1

Inverse: 1/x (x^-1)

Rule: You must drop 0 because 0 has no reciprocal

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Symmetric groups (S_n)

Identity: The “do nothing” permutation

Inverse: Flip the cycles backward

Vibe: Nonabelian for n geq 3

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