- #1

cragar

- 2,552

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to prove that their must be a larger infinity.

we know countable sets have measure zero because I could just start by making

boxes around each number and then add up their widths.

For the first number I will make a box that has width [itex] \frac{\epsilon}{2} [/itex]

and then each box will have half the width of the previous box.

so the sum will be [itex] \epsilon(1/2+1/4+1/8...) [/itex]

and i can make [itex] \epsilon [/itex] as small as I want.

This proof comes from Gregory Chaitin.

If the reals were countable they would have measure zero, but we know this isn't true

because the reals have positive width. Can i do this to prove there is a larger infninty than countable.