Partition for the equivalence relation of a parabola

[0131413]

Homework Statement

Let f: R -> R, x -> x^2

What does the partition for the equivalence relation of this function look like?

Homework Equations

The Attempt at a Solution

Uh...I have no idea. Sorry, the book only has examples of like integers from modulo n, if anybody could just point me in the right direction it would be greatly appreciated. :)

 

[tiny-tim]

hi 0131413!

(try using the X² icon just above the Reply box )

Let f: R -> R, x -> x^2

What does the partition for the equivalence relation of this function look like?

how many elements are there in each equivalence class?

 

[0131413]

hi 0131413!

(try using the X² icon just above the Reply box )how many elements are there in each equivalence class?

In this case is there one equivalence class (depending on how the parabola is shifted) with an infinite amount of elements? From the way Wiki shows rational numbers, I played around with the parabola coordinates and is the relation something like y₀-x₀²=y₁-x₁²=y₂-x₂²=...=y_n-x_n²?

...If the above statement is really, really wrong...I'm not sure why this confuses me so much either.

²

 

[tiny-tim]

hi 0131413!

unless I'm misunderstanding the question, the equivalence relation is x ~ y iff f(x) = f(y),

and so the equivalence class containing x would be all y such that f(x) = f(y)

 

[tiny-tim]

About the problem I posted, this is what it looks like: http://img809.imageshack.us/img809/6109/33666219.png

I'm starting to think that I am misunderstanding the problem. The |-> arrow, I thought I was looking at the entire R² plane and from there I needed to find a way to represent f(x) = x²?

And then I thought the equivalence relation would be using y₀-x₀²=y_n-x_n² and this would be reflexive/symmetric/transitive for every coordinate pair?

Please tell me where I went wrong. I have the Rosen 6th edition book btw...but we skip around and I don't know if there is just something additional I need to read. I am confused right now.

what does the R² plane have to do with it?

the question is about a function from R to R …

R² doesn't come into it …

the equivalence relation has to be on R (see my previous answer)

(and "|->" just means "goes to")

 

[0131413]

what does the R² plane have to do with it?

the question is about a function from R to R …

R² doesn't come into it …

the equivalence relation has to be on R (see my previous answer)

(and "|->" just means "goes to")

Is the relation abs(x) = abs(y)?

...Are the equivalence classes to look like [x] = {-x, x}? :uhh:

 

[tiny-tim]

...Are the equivalence classes to look like [x] = {-x, x}? :uhh:

yes!

(except, of course, for {0} )

 

[0131413]

yes!

(except, of course, for {0} )

Tyvm. After reading the chapter I was so confused at first, but with your words I had a lightbulb-goes-on-moment and now everything makes sense. Wish I could give you a hug. :!)