{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

definitionofZ

# definitionofZ - Math 230 E The Denition of Z Fall 2011 Drew...

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

Math 230 E Fall 2011 The Definition of Z Drew Armstrong Here’s a joke definition of the integers: Z := { . . . , - 2 , - 1 , 0 , 1 , 2 , . . . } . We all “know” the basic properties of this set because we’ve been fooling around with it since childhood. But if we want to prove anything about Z (which we do) then we need a formal definition. First I’ll give a friendly definition. This just states everything we already “know” in formal language. As you see, it’s a bit long. Afterwards I’ll give a more efficient, but more subtle, definition of Z . Friendly Definition. Let Z be a set equipped with an equivalence relation “=” defined by a Z , a = a (reflexive) a, b Z , a = b b = a (symmetric) a, b, c Z , ( a = b AND b = c ) a = c (transitive), a total ordering ” defined by a, b Z , ( a b AND b a ) a = b (antisymmetric) a, b, c Z , ( a b AND b c ) a c (transitive) a, b Z , a b OR b a (total) and two binary operations a, b Z , a + b Z

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

View Full Document
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