MATH135 Lecture Notes - Open Formula, Natural Number, Contraposition

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Wentang Kuo

Document Summary

Objective: learn the basic structure of quanti ers, and how to use object, Existential quanti er: there is, there are, there exists, it has, et cetera. Universial quanti er: for all, for each, for every, for any, et cetera. The word existence is to emphasize that we are looking for a particular math- ematical object. The word universal is to emphasize that we are looking for a set of mathematical objects. There exists an x in the set t such that f (x) is false. For every x in the set r, g(x) is false. In general, mathematicians prefer symbols rather than writing out existence and universal. Thus, the symbol stands for there exists. the symbol stands for for every. A quanti er can be either existential or universal. A set contains the domain of the variable. An open sentence that is involved with the variable. There exists an integer c so that n = cm.