Which Number Is In The Cantor Set?

Probability Level 2

Of the given answer choices, which number is in the Cantor set ?

107 364 \frac{107}{364} 111 364 \frac{111}{364} 113 364 \frac{113}{364} 115 364 \frac{115}{364}

Sameer Kailasa by Sameer Kailasa , 25, USA

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3 solutions

Ciel Tao
Nov 27, 2019

Just trying to convert the numbers in base 3. Waiting for a solution...

0 Helpful 0 Interesting 1 Brilliant 0 Confused
Edgar Santos
Aug 26, 2019

If you notice, the only numerator that is divisible by 3 is 111. Also, 111 is the only number of the four choices to not contain a two in base-3. I hope this helps someone figure a proof.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Li O Boom
Apr 16, 2019

I tried converting the numbers in base 3 and waited until there was a 1 which told me that that number couldn't be in the cantor set. Can sb explain a way of actually proofing that a number is in the set?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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