- #1

- 19

- 0

## Homework Statement

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

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

- Thread starter happybear
- Start date

- #1

- 19

- 0

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

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

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 961

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

- 19

- 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!

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

Science Advisor

Homework Helper

- 41,833

- 961

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

- 19

- 0

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

- Last Post

- Replies
- 3

- Views
- 2K

- Replies
- 5

- Views
- 613

- Replies
- 3

- Views
- 7K

- Replies
- 6

- Views
- 650

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 1K

- Replies
- 9

- Views
- 672

- Last Post

- Replies
- 3

- Views
- 4K

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 13

- Views
- 2K