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Why there is no interior points in a Cantor set? Please explain me in detail.

- Thread starter bedi
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- #1

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Why there is no interior points in a Cantor set? Please explain me in detail.

- #2

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What did you try already?

- #3

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- #4

lavinia

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What is the measure of the Cantor set?

- #5

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I don't know that measure thing yet...

- #6

lavinia

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OK. Tr describing the Canor set in the trinary system.I don't know that measure thing yet...

- #7

Bacle2

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their base-3 expansion. Now try to show,given x in C --so that there are no

1's in the decimal expansion of x -- that, no matter how close you go about x in

(x-e,x +e ) , you will hit a number y in (x-e,x+e) ,whose decimal expansion _does_

have a 1 in it . Hint: you can cut-off the decimal expansion of x at any point,

as far back as you want.

- #8

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Thank to all of you. But 1/3 is included in the cantor set and in trinary it's 0.1 isn't it? I see there is no finite trinary number in the set but why is 0.1 included?

edit: Now I think I'm okay. In the trinary number system, 1/3 can be written not only as 0.1 but also as 0.222222...

edit: Now I think I'm okay. In the trinary number system, 1/3 can be written not only as 0.1 but also as 0.222222...

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