Lecture-14

Lecture-14 - Lecture 14: Functions June 21, 2010 A set is a...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 14: Functions June 21, 2010 A set is a collection of things. All mathematical objects are sets. Usually, they have some additional structure. One kind of structure that we find in many of the sets that occur in mathematics is the presence of operations , such as + or . Another kind of structure is the relation of order . Set theory is a branch of mathematics that was invented somewhat over 100 years ago. The purpose of set theory is to study the properties of sets apart from any additional structure. Two sets are equivalent (from the point of view of set theory) if they can be put into a one-to-one correspondence, with every element of the first set corresponding with exactly one element of the second, and every element of the second set receiving correspondence from exactly one element of the first. One of the first great observations of set theory was that the set of rational numbers Q is equivalent to the set of integers Z , but not to the set of real numbers Z .....
View Full Document

Page1 / 2

Lecture-14 - Lecture 14: Functions June 21, 2010 A set is a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online