Finite, countably infinite, or uncountable

Printable View

• March 23rd 2011, 03:24 PM
JohnM25
Finite, countably infinite, or uncountable
Determine, with justification, whether each of the following sets is finite, countably infinite, or uncountable.

a) { $x \in Q | 1 < x < 2$ }

b) { $m/n | m, n \in N, m < 100, 5 < n < 105$ }

I am lost. Not sure how to approach these problems!

Thanks.
• March 23rd 2011, 03:37 PM
Plato
Quote:

Originally Posted by JohnM25
Determine, with justification, whether each of the following sets is finite, countably infinite, or uncountable.
a) { $x \in Q | 1 < x < 2$ }

b) { $m/n | m, n \in N, m < 100, 5 < n < 105$ }

For part a) A subset of a countable set is countable. Is it infinite?

Part b) is unreadable.
• March 25th 2011, 08:40 AM
Deveno
part b) given that the possible values of m (let's call this set A) are finite in number, and likewise for the possible values of n (call this set B), can you see that your set is smaller than AxB?

what can you say about the size of AxB when A and B are finite? can you think of a way to map AxB to your set that is onto, proving that your set MUST be smaller?