Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,336

hi daydoe12

Welcome to the forum.

How about

Bob

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Hi daydoe12

*Last edited by anonimnystefy (2012-11-27 02:20:37)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,336

Good answer, Stefy.

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Hmmm... I thought there was another reason.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,336

Which was ... ?

Bob

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

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

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

how did you arrive at that answer

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,336

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

Offline

**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

anonimnystefyLegendary Memberb how did you arrive at that answer

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

Hi daydoe12

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

Here lies the reader who will never open this book. He is forever dead.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,336

Thank you Stefy.

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

Bob

Offline

**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

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...

Here lies the reader who will never open this book. He is forever dead.

Offline

Pages: **1**