What is a number? That's a good question and lucky it is, or we'd be declaring that ``what'' is a number, when it's not. It's plainly being a ... oh, seems like it's being all pronoun-y. Yes, let's call it a pronoun. And that clearly won't do. Whatever you may think numbers are or what adverbs and adjectives may be they certainly aren't pronouns. Well, with one exception, that being one. But one's pronoun use is limited by it conveying to the audience that the one user passed on perhaps forty years ago while hectoring Parliament about the lessons of the Suez crisis. One can dismiss it for these purposes, but it will sneak back in unless the screens over the windows are intact.
Putting aside the question of what is a number we can look at what are numbers, as a general thing? And there are numbers all over, especially where we haven't vacuumed because they make these unpleasant rattling numbers in case a serif on the 1 or the 7 bangs the hoses. That seems like a solid starting point until someone points out those are numerals we're picking up, not numbers, and there's a very important difference we can't even start to care about. Then we realize a number is just one example of numbers, but putting us back in trouble with ``one'' and the Suez crisis. This is about when one starts hiding under the bed and swatting at passers-by.
And yet numbers we find all over the place, some ineffable trait binding together --- for the example of ``three'' --- branches of government, Marx brothers, wheels on a defective car, penny operas, and players on a baseball team if you ignore the fourth and every one after that. They must have something in common, but what is hard once you've started thinking of ``three'' to wonder what else there might be. They share having e's, for example, and they all have some letter formed by a loop and a vertical line. Can we from this conclude that three is a letter formed by a loop and a vertical line?
Not really, since the loop and vertical line thing sounds like the equipment for one of those games they played in the 18th century before fun was invented, and it seems like it applies to 9 in the right typefaces anyway. Could the existence of a number depend on what typeface it's done in? In that case, what typeface guarantees the existence of a fictional number such as ``thworb''? Probably Zapf Dingbats, although one might hold it against Comic Sans, which gets a lot of that.
Since we've found ``three'' is this abstract quantity and good luck finding where we found that, we wonder: is the ``three'' that you perceive the same ``three'' that someone else perceives? Might what you call ``three'' be what I see as ``four''? That's imaginable, if you've been watching the later Marx Brothers movies while I've been watching the ones with Zeppo. I seem to come out ahead on that count, since while you may be watching movies made after the discovery of how to record sound so the dialogue can be made out, you're stuck with fewer Marx Brothers whose names feature those precious loop-and-vertical-line characters.
In fact since Zeppo has two such characters (and more if you're writing in cursive and don't remember how to make the Z) (it's made rather like the G, which you also don't remember), this brings my three-ness of Marx Brothers up to three threes, or nine three Marx Brothers, adding up to twelve, whose digits themselves add to three. I'm almost embarrassingly overflowing in three-ness. Clearly, you'll never catch up, and probably have to watch Room Service too.
Thus, our answer: a number is what you get from calling something's GetNumber() function. For numbers describing the abstract, such as ``how much it would cost a knight or senator of the Roman Republic to replicate the functionality of an iPod'', instantiate a specific example of that entity and use it for reference. Putting all this worry into it seems kind of silly, or as numbers would put it, ``3''.
Trivia: The 1923 marriage of the duke of York was the first time a prince of the royal house had been married in Westminster Abbey in five centuries. Source: The Invention Of Tradition, Editors Eric Hobsbawm, Terence Ranger.
Currently Reading: A Splendid Exchange: How Trade Shaped The World, William J Bernstein.