Definition of binary operation in English:
A mathematical operation, such as addition or multiplication, performed on two elements of a set to derive a third element.
- Addition is a binary operation, because ‘5 + ‘doesn't mean anything by itself.
- Group theory studies not a single structure, but a type of structure, the pattern common to collections of objects with a binary operation, an identity element thereon, and inverses for each element.
- We want this to be a field, that is, that for all numbers a, b, c in * R with two binary operations, + and x (addition and multiplication) the following field axioms should hold: a + b and a x b are both in * R
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