Sunday, 17 May 2015

Real valued function which is continuous only on transcendental numbers

First of all, I am sorry for asking this question.



We know that R is uncountable. And also the set of all transcendental numbers is uncountable.
How can I construct a function f(x) on R which is continuos only at transcendental numbers? Is it possible?



Thanks in advance.

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...