Page 49 - 'Blast_Into_Math

Blast into Math! ets of nummers: mathematical plaagrounds

Proof: You can prove this proposition very similarly to the LUB Proposition, so to help you practice
proving propositions, you will prove the GLB Proposition as an exercise at the end of this chapter. Most
mathematical research is achieved through mathematical teamwork of two or more mathematicians
working together. When we work together, it’s similar to playing baseball, in which each player has a
certain skill which he or she contributes to the team, like pitching, hitting, or catching. We must each
train individually just as each baseball player trains to maintain his or her skills and physical fitness. In
mathematics research, this mathematical training is spending time alone working on problems, which
you do when you solve the exercises in each chapter. Then, you bring your skills to the mathematical
team, and our teamwork proves the proposition!

The unique smallest element of a set S is its greatest lower bound, or GLB.

Definition 3.3.5 Let S be a non-empty set of rational numbers which is bounded below. If there exists
a lower bound B which is greater than or equal to all other lower bounds of S , then B is called the
greatest lower bound of S .

The greatest lower bound is exactly that: it is the largest or greatest lower bound.

49