- #1
Askhwhelp
- 86
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1) For the following choice of A, construct a function f: R → R that has discontinuities at every point x in A and is continuous on the complement of A.
A = { x : 0 < x < 1} My function is f(x) = 10 if x in (0,1) and Q and f(x) = 20, if x in (0,1) and irrational number, f(x) = 30, elsewhere. By the way, this is piece wise function.
Does this example work?
Also for A = {1/n: n is natural number) Does f(n) = 10 if 1/n is natural number and f(n) = 0, elsewhere work?
A = { x : 0 < x < 1} My function is f(x) = 10 if x in (0,1) and Q and f(x) = 20, if x in (0,1) and irrational number, f(x) = 30, elsewhere. By the way, this is piece wise function.
Does this example work?
Also for A = {1/n: n is natural number) Does f(n) = 10 if 1/n is natural number and f(n) = 0, elsewhere work?