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## #1 2012-11-27 13:40:18

daydoe12
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Define a bijection between the sets [-2,8] and [3,5]. Prove your function is actually a bijection.

## #2 2012-11-27 20:13:05

bob bundy
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hi daydoe12

Welcome to the forum.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #3 2012-11-28 01:18:38

anonimnystefy
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Hi daydoe12

Last edited by anonimnystefy (2012-11-28 01:20:37)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #4 2012-11-28 06:43:44

bob bundy
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I think yours is correct and I have misunderstood what is wanted.

I'll leave the post as a reminder to me to read the question!

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #5 2012-11-28 08:08:20

anonimnystefy
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Hmmm... I thought there was another reason.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #6 2012-11-28 08:10:52

bob bundy
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Which was ... ?

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #7 2012-11-28 08:16:14

anonimnystefy
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Doesn't matter. I hope we solved the OP's problem.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #8 2012-11-29 15:39:02

daydoe12
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how did you arrive at that answer

## #9 2012-11-29 18:59:53

bob bundy
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Stefy just looked for a formula of the form y = mx + c so that when x = -2, then y = 3, and similarly when x = 8, y = 5.

My answer used a similar idea but I think his is the right way.

If you think about the straight line graph this produces, every point between -2 and 8, will map onto every point between 3 and 5

And the mapping is reversible.

To prove it, you'd have to show the mapping is 1:1 in both direcctions, and that a point inside the first interval maps to a point inside the resulting interval.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #10 2012-11-30 14:30:39

daydoe12
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anonimnystefyLegendary Memberb how did you arrive at that answer

## #11 2012-12-01 01:48:15

anonimnystefy
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Hi daydoe12

Bob explained very well in post #9. I don't think I could any better at explaining it.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #12 2012-12-01 03:45:41

bob bundy
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Thank you Stefy.

And there was me, about to award you the "Teacher of the Month Award"

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #13 2012-12-04 14:30:49

daydoe12
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I have tried finding the form using the y=mx+b formula and i cant figure out how she got x+17/5

## #14 2012-12-04 16:05:51

bobbym

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Hi daydoe12;

You have -2 -> 3 and 8 -> 5 so call x=-2 and y =3 in the first equation and x = 8 and y = 5 in the second.

When you solve that you get m = 1/5 and b = 17 / 5. Now plug in to the first equation.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #15 2012-12-04 20:52:11

anonimnystefy
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#### bob bundy wrote:

Thank you Stefy.

And there was me, about to award you the "Teacher of the Month Award"

Bob

I hope you are kidding.

Hi daydoe12

I'm male, not female...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment