- #1

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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

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- Thread starter happybear
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- #1

- 19

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For all real number x, can you find a function f and g such that

sup|f(x)-g(x)|=0

- #2

HallsofIvy

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What have you done on this problem yourself? In particular, what does sup |f(x)- g(x)|## 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

- #3

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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!

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

- #4

HallsofIvy

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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

Suppose f were NOT equal to g. Then there must exist some x such that [itex]f(x)\ne g(x)[/itex]. Let M= |f(x)- g(x)| for

- #5

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so does that mean that no matter whether X is compact or not, there is no such a function?

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