Section 5.6 ChapterĀ 5 Summary
Subsection Important Definitions
Subsection Important Theorems and Results about Sets
Subsection Important Proof Method
Subsubsection The Choose-an-Element Method
The choose-an-element method is frequently used when we encounter a universal quantifier in a statement in the backward process of a proof. This statement often has the form
For each elemet with a given property, something happens.In the forward process of the proof, we then choose an arbitrary element with the given property.
Whenever we choose an arbitrary element with a given property, we are not selecting a specific element. Rather, the only thing we can assume about the element is the given property.For more information, see The Choose-an-Element Method.