Graduate Understanding Cantor set C in Ternary form with 1/n factor in front C

[cbarker1]

TL;DR

I am trying to comprehend the Cantor set C with a 1/n factor in base 3

Dear Everybody,

I am confused by $1/n C$, where C is a cantor set in base 3 and $n\geq2$. I can understand the construction of the normal Cantor set.

How do I comprehend this set with this extra condition. Do I multiply the set with $1/n$ or not?

Thanks,
Cbarker1

mentor note: adjusted latex to use double # instead of single #

 

[pbuk]

Understanding Cantor set C in Tetany form with 1/n factor in front C

I have never seen the word "Tetany" before: do you mean "ternery"? Even with this correction I'm afraid the rest of the post doesn't make much sense to me.

Do you have a reference for the ideas you are talking about?

If not, can you provide a more complete description of the set avoiding ambiguous notation like $1/n C$ which whether in $\LaTeX$ or plain text can mean either $\frac{1}{nC}$ or $\frac{1}{n}C$. Perhaps you could start by rephrasing "The Cantor ternary set is created by iteratively deleting parts of a set of line segments. One starts by deleting the open middle third $\left ( \frac{1}{3} , \frac{2}{3} \right)$ from the interval $[ 0 , 1 ]$."

 

[Mark44]

have never seen the word "Tetany" before: do you mean "ternery"?

I changed "tetany" in the thread title to "ternary," as my best guess as to what the OP was trying to convey.

Also, perhaps the "1/nC" (with same complaint about what 1/nC actually means) is meant to convey the level of middle third deletions. Again, that's a guess. If so, with n = 1, we would have the two subintervals [0, .1] and [.2, 1], using base-3 fractions. With n =2, we remove the middle third from each of the two previously listed subintervals. This would produce four subintervals: [0, .01], [.02, .1], [.2, .21], and [.22, 1], again using base-3 fractions.

And so on.

 

[cbarker1]

your guesses are right. I want that word Ternary and $(1/n)*C$.

 

[pbuk]

OK, so how much of the set do you remove at the first iteration?

How much at the second?
...
How much at the $n$th?
...

How much in total as $n \to \infty$?