The real number system and field axioms
General · Mathematics
Study notes
Q: Using field axioms, prove 0×a = 0 and (-1)×(-1) = 1. 0×a = (0+0)×a = 0×a+0×a. Cancel 0×a: 0 = 0×a ✓. (-1)+1 = 0. Multiply by -1: (-1)(-1)+(-1)(1) = 0. (-1)(1) = -1: so (-1)(-1) = 1 ✓! (Axioms prove familiar facts!)