PHILOS 146 Lecture Notes - Lecture 9: Richard Dedekind, Binary Relation, Irrational Number
Document Summary
1. line has a property of completeness which rational numbers don t. If there is such a point x, it produces the cut c b: definition: identity conditions for reals, given real numbers a and b, which produce cuts (a1, a2) and (b1, b2) A1 = b1, ie, every element of a1 is in b1 and vice versa, or. A1 and b1 differ by exactly one element respectively, a = b iff a. i. a. ii. A1: properties of the reals, transitivity of b and b>g, then a >g, density of the reals. If a =/= g, then there are infinitely many reals b s. t. > a: proof outline, observe kr determines a cut in kq on the rationals, kq corresponds to a real number a, show that a uniquely produces kr, proof, notice that kr determines a cut kq a. i.
