Fanidan taqdimot

Let Vect3(R) denote the vectors in 3-space. Then the vector cross product × is a binary operation on Vect3(R). Note that the scalar product · does not define a binary operation on Vect3(R).

• Let Vect3(R) denote the vectors in 3-space. Then the vector cross product × is a binary operation on Vect3(R). Note that the scalar product · does not define a binary operation on Vect3(R).
• Let A be a set and let 2A be its power set. The operations ∩, ∪, and + (symmetric difference) are all important binary operations on 2A.
• Let S be a set and let Sym(S) be the set of all permutations on
• Then function composition ◦ defines a binary operation on Sym(S). We really should prove this. Thus let σ, τ : S → S
• be permutations; thus they are one-to-one and onto. We need to show that σ ◦ τ : S → S is also one-to-one and onto.
• σ ◦ τ is one-to-one: Assume that s, sr ∈ S and that σ ◦ τ (s) =
• σ ◦ τ (sr). Since σ is one-to-one, we conclude that τ (s) = τ (sr).