MATH135 Lecture Notes - Mathematical Induction, Irrational Number, Contraposition

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Janelle Resch

Document Summary

In math, we have a couple of key words/phrases used in small statements. Depending on the quantifier used certain proof techniques can be used to prove the statement. Existential quantifiers: there are, there is, there exists. These are existential quantifiers and we denote them with we used when we are looking for math objects. Basic structure: there is some object" in the set where the object was taken" with a certain property" such that something happens". For every object" with a certain property", something happens. Universal quantifiers: for all, for each, for any. These are universal quantifiers and we denoted them . When " is used we are looking for a set of objects that all share the same property. Ex: there exists an x in the set s such that p(x) is true b) X y, (x y), x, y ez. That integer is greater than or equal to all integers.