We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
GO TO SAT PREP GO TO ACT PREP
Types of Numbers

Types of Numbers

At a Glance - Counting Irrational Numbers


The reason we can't list the real numbers between 0 and 1 in a sequence is that there are too many irrational numbers. Nice going, guys. Way to ruin it for the team.

Think about it: we can list the rational numbers. If we could also list the irrational numbers, then we could list the real numbers by interweaving the two lists, taking one rational number, one irrational number, one rational number, etc. We might even be able to macramé ourselves an attractive lampshade.

Anyway, our lists would look like this:

rational numbers: r1, r2, r3,...

irrational numbers: s1, s2, s3,...

real numbers: r1, s1, r2, s2, ....

Since we can list the rational numbers but not the real numbers, we must not be able to list the irrational numbers either. What a buzzkill.

People who Shmooped this also Shmooped...

Advertisement