# 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

## closed as not constructive by fpqc, Thomas, Arthur Fischer♦, Javier Álvarez, rschwiebJan 26 '13 at 15:51

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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.