- #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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- 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

Science Advisor

Homework Helper

- 43,008

- 974

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

Science Advisor

Homework Helper

- 43,008

- 974

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?

Share:

- Replies
- 3

- Views
- 375

- Replies
- 0

- Views
- 12

- Replies
- 2

- Views
- 815

- Replies
- 5

- Views
- 709

- Replies
- 5

- Views
- 787

- Replies
- 3

- Views
- 550

- Replies
- 3

- Views
- 614

- Replies
- 5

- Views
- 366

- Replies
- 9

- Views
- 399

- Replies
- 2

- Views
- 902