MAT134Y5 Lecture Notes - Lecture 2: Kolmogorov Space
Document Summary
A function f from a set d to a set y is a rule that assigns a unique element f(x) to each element x e d. Every element in d must be assigned something. Not every element in y must be assigned something. The range is the set of all possible images (all elements of y that have a f(x) value). Examples: f: (0,infinite) -> r, f(x) = 1/x. F(2) = 1/2, f(2/3) = 3/2, f(-5) is undefined because the domain starts at 0: g:[-5,5] -> [0,infinite), g(x) = |x| Target space is [0,infinite). g(0) = 0, g(-pi) = pi, g(1. 7) = 1. 7: h:r->r, h(x)=x^2+3 h(-5) = (-5)^2 + 3 = 28. No matter what the value of x is, h(x) will never be equal to 0. The target space is then taken to be r. The natural domain of f(x) = square root of x would be x > 0.
