{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lec5 - Math 117 5 Cardinality Denition 5.1 Two sets S and T...

This preview shows page 1. Sign up to view the full content.

Math 117 – April 12, 2011 5 Cardinality Definition 5.1. Two sets S and T are called equinumerous, denoted by S T , if there exists a bijection from S onto T . Equinumerosity defines an equivalence relation on families of sets. The equivalence classes separate sets into classes of equal size, and we associate cardinal numbers to each class for the size of the sets in that particular class. Definition 5.2. A set S is said to be finite if there exists n N and a bijection f : I n = { 1 , 2 , . . . , n } → S . If a set is not finite, it is called infinite A set S is called denumerable, if there exists a bijection f : N S . If a set is finite or denumerable, it is called countable. Countable sets are those whose elements can be indexed by the natural numbers, i.e. S = { s 1 , s 2 , . . . } . The indexing is given by the bijection f : I n S or f : N S , in which case s 1 = f (1), s 2 = f (2) , . . . , s n = f ( n ) , . . . . One can show that any subset of a countable set is also countable.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern