Real Variables Problem?
Can somebody help me with this please??? I thought it would stand out to me but I guess not :-(
R stands for real numbers.
This is for my Real Variables class :-)
Let f,g be continuous from R to R, and suppose that f(r)=g(r) for all rational numbers r. Is it true that f(x)=g(x) for all x in R.
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Yes. Let h(x) = f(x) - g(x). Then h is continuous and h(r) = 0 for all rational r. For any real number x, there is a sequence r_n of rational numbers such that r_n ---> x. Since h is continuous, h(r_n) ---> h(x). Since h(r_n) = 0 for all n, h(x) = lim h(r_n) = 0.
placed the entire fraction decrease than the unconventional and cancel out the B interior the denominator so as that the fraction is 108B^2 decrease than the unconventional and simplify it from there you are able to placed a B on the outdoors of the unconventional by way of fact there are 2 of them and you would be able to pull out a 4 and a three that get elevated all jointly so which you have 12B outdoors and 3 interior the unconventional and that's your very final answer