MATH 2360Q Lecture 3: Chapter 2 Cont.

• School: UConn
• Department: Mathematics
• Course: MATH 2360Q
• Professor: Scott Zimmerman

Document Summary

Ex: there is some irrational x so that x2 is rational. To prove this, just find one x satisfying this statement. (square root. To prove this, show that it is true for every x. Not (there exists x such that p(x)) = for all x, (not p(x)) The negation of the first statement above is for all irrational x, x2 is irrational . For all irrational x, x2 is irrational (not p(x)) Not (for all x, p(x)) = there exists x such that (not p(x)) The negation of the second statement above is there exists a real number x such that x2 <0 . Proving that there is a unique x satisfying p(x) requires you to show that two different x"s which satisfy p(x) cannot exist. Usually, we do this by assuming that there are two and showing that they must be equal. There is a unique real number x such that 4x+5=12. Only 1 number that satisfies this equation.