- #1
stunner5000pt
- 1,461
- 2
Let f ( x ) = {0, if x = 1/n for some natural number n
or 1, otherwise
Note: Natural number would refer to the set of positive integers Z+ that is 1,2,3,...
Prove that this function is integrable on [0,1] and it's integral is 1
Certainly there are an infinite number of dicontinuities and nearly all of the function lies in the domain of [0,1]. But is the set of Inverse Naturals (1/n) (postive integers) bigger than the set of irrationals?
Someone recommended using the Robustness of the Reimann Integral
Let g and f be two functions defined on [a,b], and suppose
that the set of numbers in [a,b] at which the functions do not
take the same value (at which they "differ") is finite.
or 1, otherwise
Note: Natural number would refer to the set of positive integers Z+ that is 1,2,3,...
Prove that this function is integrable on [0,1] and it's integral is 1
Certainly there are an infinite number of dicontinuities and nearly all of the function lies in the domain of [0,1]. But is the set of Inverse Naturals (1/n) (postive integers) bigger than the set of irrationals?
Someone recommended using the Robustness of the Reimann Integral
Let g and f be two functions defined on [a,b], and suppose
that the set of numbers in [a,b] at which the functions do not
take the same value (at which they "differ") is finite.