1. ## discrete

any set in R or C, which is discrete should be countable.(statement from the standard book)

is it correct?

then
what can you say about cantor set which is uncountable?
is it not discrete?

2. ## Re: discrete

Originally Posted by saravananbs
any set in R or C, which is discrete should be countable.(statement from the standard book)
is it correct?
then what can you say about cantor set which is uncountable? is it not discrete?
I think that you are using the word discrete in different ways.
" More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets."
That is a quote from this webpage
That a quite different from a discrete topology or discrete metric.

What is you understanding of discrete?

3. ## Re: discrete

no. every point of the cantor set is a limit point: no matter how small an open interval around any point of the cantor set you select, there are always other points of the cantor set within that interval. even though the cantor set appears to be a finely atomized "dust", the elements "accumulate" about the endpoints of the "outer thirds" we keep at each iteration.

4. ## Re: discrete

Originally Posted by saravananbs
any set in R or C, which is discrete should be countable.(statement from the standard book)

is it correct?
Define "discrete set".

then
what can you say about cantor set which is uncountable?
is it not discrete?