Logic and Sets by NIRUCH IMARROM https://padlet.com/6231306082/4uepmw0bkeyd7pvy Made with the strength to succeed en-us 2021-09-11 21:55:34 UTC 2021-09-11 21:58:25 UTC hello@padlet.com 6231306082 https://padlet.com/6231306082/4uepmw0bkeyd7pvy/wish/1732987301 A set is a collection of objects; any one of the objects in a set is called a member or an element of the set. If a is an element of a set A we write a∈A.

 

Some sets occur so frequently that there are standard names and symbols for them. We denote the real numbers by R, the rational numbers (that is, the fractions) by Q, the integers by Z and the natural numbers (that is, the positive integers) by N.

 

There is a natural relationship between sets and logic. If A is a set, then P(x)="x∈A'' is a formula. It is true for elements of A and false for elements outside of A. Conversely, if we are given a formula Q(x), we can form the truth set consisting of all x that make Q(x) true. This is usually written {x:Q(x)} or {x∣Q(x)}.

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