# Defining a mathematical doodad [closed]

When you define something in mathematics, can you do no appealing to what it does?

For example, I can define the a function by its outcome. f(x) = 2x is something that doubles x. But, I wouldn't be able to tell you what it is.

In contrast to real life doodads where you can define, for example, a knife by its shape + material or by what it does (cut).

Are mathematical doodads defined just by that, by what they do?

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What does doodad mean ? –  Amr Jan 26 '13 at 13:10
You are going to need to express yourself a little more clearly if you expect to get a reasonable answer. I can't really make heads or tails of what you want. –  Tim Seguine Jan 26 '13 at 13:14
@Amr doodad 1) An un-namable gadget of some sort, possibly highly technical. –  Did Jan 26 '13 at 13:15
Your example of $f(x) = 2x$ doesn't seem to help your point. You are definining $f$ by what it does, but you seem to suggest that this is not how things are done in mathematics. Also, I, and the Oxford English Dictionary, would define a knife to be "an instrument composed of a blade fixed into a handle, used for cutting or as a weapon." Part of that definition is what the knife does, making the point that (I think) you are trying to make, less agreeable. I suggest editing your post and putting some more detail in as I'm not really sure what it is you are asking at the moment. –  Michael Albanese Jan 26 '13 at 13:16
And doodad: 2) an often small article whose common name is unknown or forgotten: gadget. –  Did Jan 26 '13 at 13:19
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## closed as not constructive by fpqc, Thomas, Arthur Fischer♦, Javier Álvarez, rschwiebJan 26 '13 at 15:51

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## 1 Answer

The difference you see between mathematics and "real life" is based on a misperception both of mathematics and of "real life".

In mathematics, not everything is defined in terms of what it "does". For instance, an even number is an integer such that there is no remainder when it is divided by $2$ – no "doing" there.

On the other hand, in "real life", everything is defined by what it "does", because that's the only access you have to it. What you call the knife's "shape" and "material" is an aspect of what the knife "does" to other stuff you let it interact with, be it light or X-rays or neutrons or gravitons.

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