MATH 13 Lecture Notes - Rational Number, Equivalence Class, Spacex
Document Summary
Here we explore di erent examples related to the notion of a well-de ned function. We as- sume the reader knows the de nition of a well-de ned function, and is confortamble with the set. X/e = {[x] : x x} (that is, the induced partition of an equivalence class). De ne the (equivalence relation) r on x by: arb i a and b were born in the same month m {1, . There are a total of 12 equivalence classes, so we can say: Where ci = {x x : x was born in the i-th month. Also, c1 c2 c11 c12 = x. This partitions the set of humans in 12 disjoint nonempty sets. Now we consider possible operations with domain x/r, and see if they are really well-de ned (unambiguous). Operation 1: f : x/r n, b([x]) = age of x(cid:48)(cid:48).
