## cantor set = set of all what in base 3?

For the discussion of math. Duh.

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aguacate
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### cantor set = set of all what in base 3?

Reading through my notes in my Real Analysis class, I wrote down that the cantor set P = {x \in \R | x has n 1s in its base three expansion}. I guess I forgot to put what n was. Is n any element of Z? Did I mean to write 'inf'? Little help please?

GreedyAlgorithm
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### Re: cantor set = set of all what in base 3?

IIRC n means "a finite number" here.

ETA: I do not recall correctly and did not do any checking of my recollection and it shows.
Last edited by GreedyAlgorithm on Fri Oct 26, 2007 5:17 am UTC, edited 1 time in total.
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Buttons
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### Re: cantor set = set of all what in base 3?

I don't think you forgot to define n. I think you dropped an 'o'.

Every number in the Cantor set can be written with no 1s in its ternary expansion.

(Note that 1/3 = 0.13 = 0.02222222...3, so 1/3 is in the Cantor set even though one of the two ways to write it violates the above.)

Hix
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### Re: cantor set = set of all what in base 3?

Buttons is right on. If you're used to thinking of the Cantor set as "Start with [0,1] and repeatedly remove the middle thirds of all segments", then notice that the first iteration removes everything that must be written in ternary with a 1 right after the radix point, the second iteration removes everything that must be written with a 1 in the _next_ position, etc.