cantor set = set of all what in base 3?

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

aguacate
Posts: 209
Joined: Fri Feb 16, 2007 10:29 pm UTC

cantor set = set of all what in base 3?

Postby aguacate » Fri Oct 26, 2007 4:24 am UTC

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?
Image

GreedyAlgorithm
Posts: 286
Joined: Tue Aug 22, 2006 10:35 pm UTC
Contact:

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

Postby GreedyAlgorithm » Fri Oct 26, 2007 4:49 am UTC

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.
GENERATION 1-i: The first time you see this, copy it into your sig on any forum. Square it, and then add i to the generation.

Buttons
Posts: 858
Joined: Wed May 02, 2007 3:27 pm UTC
Location: Somerville

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

Postby Buttons » Fri Oct 26, 2007 5:13 am UTC

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
Posts: 364
Joined: Sun Oct 15, 2006 5:46 pm UTC

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

Postby Hix » Sun Oct 28, 2007 3:33 am UTC

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.


Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 8 guests