f(x) is a function defined from Set of rational numbers Q to itself as
f(x)=x,
Is this function continuous at all rational numbers?
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f(x) is a function defined from Set of rational numbers Q to itself as
f(x)=x,
Is this function continuous at all rational numbers?
It's continous fromQuote:
Originally Posted by vms
to itself (just use
in the definition of continuity), hence also continuous when restricted to any subset. So the answer is "yes, it's continuous".
On the other hand, in response to Ene Dene's post, if f(x) is defined as constant c for all real, then f is continuous at x=c only .
I've deleted that post, after seeing your answer, becoase I thought I understood the question wrong. The question should have been more accurate.Quote:
Originally Posted by hpeOn the other hand, in response to Ene Dene's post, if f(x) is defined as constant c for all real
Anyway, I'm satisfied now :).