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### Relations in Real Life

```Date: 10/02/2012 at 11:06:31
From: Bethany
Subject: How a relation range connects to the real world

Hi,

In class we are currently learning about relations, functions, domain,
range, etc.

I know that a relation is just a set of ordered pairs, and a function is
just a type of relation.

I know that the domain is the set of all the 1st numbers, or in other
words, the x-values, and the range is the set of all the 2nd numbers, or
in other words, the y-values.

I know what these are, and a bit more. I just want to know how they relate
to the real world ... maybe with some examples of how they might help us
in life, in real life situations, so I can know the material a little
better?

Can you help me connect mathematical relations with the real world?

Thank you!

```

```
Date: 10/02/2012 at 19:48:43
From: Doctor Ian
Subject: Re: How a relation range connects to the real world

Hi Bethany,

Can you imagine a situation where some inputs are not allowed? For
example, you might have a mapping from weight, in ounces, to postage
required. Can you have a negative weight for that? No. So that would be a
restriction on the domain of the mapping, right?

What about a situation where, no matter what input you have, there are
some outputs you can't get? For example, you might be mapping engine size
to maximum speed. Are there some speeds that can't be attained? We know
that nothing can go faster than the speed of light, but we might have a
lower limit than that. So this would be a restriction on range, right?

The idea of a mapping is very, very general, and goes beyond math. For
example, you dial a particular phone number, and you expect a certain
person to answer, right? That's a mapping -- from phone number to person.
Are there some "numbers" that wouldn't connect to any phone? Sure. Are
there some people who don't have a phone? Sure.

The fundamental idea behind all this is just realizing that sometimes
inputs and outputs won't make sense, and you want to stay aware of that,
so you don't get caught treating nonsense as if it's meaningful. That
awareness is an important skill to have, even if you never use algebra
once you're out of school.

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/

```

```
Date: 11/05/2012 at 09:29:10
From: Bethany
Subject: Thank you (How a relation range connects to the real world)

Thank you for answering my question. I understand more now.
```
Associated Topics:
High School Functions

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