Can anyone tell me how I could show that the following set is countable?

Natural numbers and the real numbers with decimal representations consisting of all 1's?

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- Feb 8th 2009, 10:58 AMvexikedCardinality
Can anyone tell me how I could show that the following set is countable?

Natural numbers and the real numbers with decimal representations consisting of all 1's? - Feb 8th 2009, 11:09 AMPlato
- Feb 8th 2009, 01:44 PMvexiked
The question is as follows:

Prove that the sets of natural numbers and the real numbers with decimal representations of all 1's are countable or uncountable. - Feb 8th 2009, 02:18 PMLaurent
Do you mean the set containing the numbers like 1111.1111111?

Here's a hint: You can identify such a number with the couple $\displaystyle (m,n)\in\mathbb{N}^2$ where $\displaystyle m$ is the number of 1's on the left, and $\displaystyle n$ the number of 1's on the right. (Actually, you should probably also consider $\displaystyle n=\infty$ as a possibility.) From there, it should be clear whether the set is countable or uncountable. - Feb 11th 2009, 05:36 PMGaloisTheory1