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A binary operator representing direct sums of vector spaces, exclusive OR in logic, or addition in cyclic groups.

\oplus image

Examples

Direct sum of vector spaces

V = V_1 \oplus V_2 \oplus V_3

Exclusive OR (XOR) operation in logic

A \oplus B = (A \land \neg B) \lor (\neg A \land B)

Group theory: external direct product

G = \mathbb{Z}_2 \oplus \mathbb{Z}_4 \oplus \mathbb{Z}_8