Equivalence Classes of Continuous Functions with a Common Value at x=4

[polarbears]

Homework Statement

Identity if it is an equivalence relationship and describe the equivalence class.

The relationship T on the set of continuous functions mapping R to R, where fTg iff f(4)=g(4)

Homework Equations

The Attempt at a Solution

It is an equivalence relationship just by inspection, but I don't understand how to describe the equivalence class.

 

[CompuChip]

"Just by inspection" is, in my mathematical opinion, not a good enough argument. You need to show that T satisfies the properties (e.g. fTf; if fTg then gTf, etc).

Let's consider a single continuous function f from R to R. Can you describe in words all functions that are equivalent to it (w.r.t T)?

 

[polarbears]

Alright--hehe yeah I was getting lazyUmm all functions that intersect this function at 4?

 

[CompuChip]

Assuming you meant: all continuous functions mapping R to R which intersect f(x) at x = 4, yes :)

So what do the equivalence classes of T look like? For example, if I asked you to write them all down like [c] = { ... }, where c is a label for the equivalence class?

 

[polarbears]

Wait so my answer wasn't right? or is it?

How about this...
The equivalence class of T are sets of all continuous functions mapping R to R which intersect f(x) at x = 4?

But then I feel like that's just restating what the equivalence relationship is in the 1st place

 

[vela]

CompuChip was just making your previous statement more precise, but his question wasn't exactly the same as asking what the equivalence classes were. He's trying to get you to make that final leap now.

All the functions in an equivalence class share a common trait. What is it that characterizes all the functions that belong to a specific equivalence class? Note this time you don't have a specific f(x) you can compare the rest to.