# math 4 10

x 1 0 1 0 1 0 1 x 1 0 1 0 1 0 1 f f(-1) A a A(-1) ⁡ a f f(-1) A a A(-1) ⁡ a x x x x 1 λ x . sin ⁡ (x+1) x ↦ sin ⁡ (x+1) x1 xn expression-in-x1-xn lambda x1 xn expression-in-x1-xn x1 xn D expression-in-x1-xn restriction lambda x1 xn expression-in-x1-xn D f g h f∘g∘h f g x f g x (f∘g) ⁡ x = f ⁡ g ⁡ x f f f ∘ f(-1) = id f domain⁡f = R f codomain⁡f = Q -1 1 image⁡sin = -1 1 x x 0 0 x 0 x x 0 { −x if x<0 0 if x=0 x if x>0 0 x 0 1 x 1 x piecewise piece 0 lt x 0 piece 1 gt x 1 otherwise x a b ⌊a/b⌋ n n! a b a/b 2 3 5 max {2,3,5} y y 0 1 y 3 max {y| y 3 ∈ 0 1 } a b min {a,b} x x B x 2 min {x 2| x∉B } 3 −3 x y x−y x y z x+y+z x 3 x 3 a b a mod b a b a⁢b n a a n x root x 2 n a root a n