- #1

- 4

- 0

## Homework Statement

Prove that the rationals as a subset of the reals can all be contained in open intervals the sum of whose width is less than any \epsilon > 0.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter zhang128
- Start date

- #1

- 4

- 0

Prove that the rationals as a subset of the reals can all be contained in open intervals the sum of whose width is less than any \epsilon > 0.

- #2

Dick

Science Advisor

Homework Helper

- 26,263

- 619

- #3

- 4

- 0

- #4

Dick

Science Advisor

Homework Helper

- 26,263

- 619

Much better, thanks. Can you write a series that converges to epsilon? If you can write a series that sums to say, 1, you should be able to write a series that converges to epsilon.

- #5

- 4

- 0

hmmm, like epsilon/(n^2+n)??

- #6

Dick

Science Advisor

Homework Helper

- 26,263

- 619

hmmm, like epsilon/(n^2+n)??

Sure, that works. I would have said sum epsilon*(1/2)^n. But whatever you like.

Share: