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Homework Statement
For all real number x, can you find a function f and g such that
sup|f(x)-g(x)|=0
What have you done on this problem yourself? In particular, what does sup |f(x)- g(x)| mean? And if you are going to put "f is not equal to g" please put it in the statement of the problem!Homework Statement
For all real number x, can you find a function f and g such that
sup|f(x)-g(x)|=0
Homework Equations
The Attempt at a Solution
What have you done on this problem yourself? In particular, what does sup |f(x)- g(x)| mean? And if you are going to put "f is not equal to g" please put it in the statement of the problem!
Strictly speaking, sup does NOT mean 'maximum', it means "least upper bound" which may or may not be a maximum. What do you mean "f approaching g"? As x approaches what value? This has to be true over all x.sup{|f-g|} means that the maximum of the value. I try to find a function f approaching g, but this eem not to be the case