Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Sizes of "infinite sets"
Name: philip a rust
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: N/A 

I have a question about what was said in the first response on note 400. How can you say that the {infinite set of all real numbers} is greater than the {infinite set of all integers}? Please go into a lot of depth for I thought I was clear on this concept. Thank You

This can't be answered in a lot of depth in only one screenful of text. But try looking up 'Cantor's diagonal argument'. The idea is that if there are as many real numbers as integers, you should be able to make a table listing in one column all integers and in the other all reals. Contor's argument shows that whenever you think you've made such a list, you can construct a real number that isn't on the list. Thus the set of real numbers is greater than the set of integers.

jan p anderson

A good source is *Advanced Calculus* by Angus E. Taylor, p 479-80.


Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory