# Mapping a: S -> T be so that any x ε S has one and only one y &#

1. Mar 29, 2009

### Gear300

mapping a: S --> T be so that any x ε S has one and only one y &#

What makes it necessary for any mapping a: S --> T be so that any x ε S has one and only one y ε T?

2. Mar 29, 2009

### slider142

Re: Mappings

That's the defining property of a being a function from S to T.

3. Mar 29, 2009

### Gear300

Re: Mappings

So it is necessary only by definition?

4. Mar 29, 2009

### slider142

Re: Mappings

It is not necessary at all. One can talk about mappings that are not functions as well. What is the context of this question?

5. Apr 1, 2009

### Gear300

Re: Mappings

I see...what I was referring to were particular types of mappings (functions), right?

6. Apr 1, 2009

### HallsofIvy

Re: Mappings

It might help if you told us exactly what you mean by "S" and "T"!

If you are referring to any sets S and T and by "mapping" you specifically meant "function", then yes, that is true simply because of the definition of "function".