MATH 1190 Lecture 11: Translating Mathematical Statements into Statements Involving Nested Quantifiers

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1190
• Professor: Laura Colmenarejo Hernando

Document Summary

Math 1190 lecture 11 notes - translating mathematical statements into statements. |f (x) l| < [1]) when the domain for the variables [1] and consists of all real numbers, rather than just the positive real numbers: here, restricted quantifiers have been used. Recall that x>0 p(x) means that for all x with x>0, p(x) is true. In other words, there is a student none of whose friends are also friends with each other. ) q(f, a)) w a f (p(w, f ) q(f, a)) w a f (p (w, f ) q(f, a)) [1]>0 >0 x(0 < |x a| < |f (x) l| < [1]): successively applying the rules for negating quantified expressions, we construct this sequence of equivalent statements [1]>0 >0 x(00 >0 x(00 >0 x(00 >0 x. (00 >0 x(0