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The Situation Room 2.0

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But I can an invent a number whose definition will include that it can't be doubled.

And I'll call it Steve. It'll create a whole new set of imaginary (but not complex) numbers who'll bring a revolution to maths :p
 
Technically, infinity can be doubled... but it's not any better than having a Magikarp use Splash.

However, if the homework assigned to me involves new sets of numbers I wouldn't object; I'll just invent a set of numbers that will let me multiply the rest of the homework with something and get zero :p
 
It does, actually. When's the last time you doubled infinity? :p
What Zexy said. Also, technically, infinity is not a number. It is a concept. An impossible concept.

Nonetheless, it is possible to talk about such abstract things as infinity, infinity -1, 2* infinity, and so forth, even though they are all, technically, still infinity.
 
Definition of number: "an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification."

So I guess it depends on whether you count an unquantifiable quantity as a quantity (as oxymoronic as that sounds).

I'd say it is, as when you refer to "infinite amount of numbers between 1.1 and 1.2" you're referring to an amount, aka a quantity.
 
Infinity doesn't actually represent an arithmetical value, though, since it cannot be represented in any means. You cannot have infinite grains of rice like you can have 1,000,539,197 grains of rice.
No matter how many grains of rice you might have, you will never, ever, have infinity grains.

All numbers can be represented in some way by numeral (0-9). Infinity cannot.
 
Infinity doesn't actually represent an arithmetical value, though, since it cannot be represented in any means. You cannot have infinite grains of rice like you can have 1,000,539,197 grains of rice.
No matter how many grains of rice you might have, you will never, ever, have infinity grains.

All numbers can be represented in some way by numeral (0-9). Infinity cannot.

This post is an example of the "No True Scotsman" fallacy. None of those qualities are necessary to be a number. Sure, the vast majority of numbers have those qualities. But it's not a requirement.
 
Definition of number: "an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification."
The definition of a number that you brought. Not me.
1. Infinity is indeed represented by a word and a symbol, but it does not represent an arithmetical value.
2. Infinity does not represent a particular quantity, since you cannot count to infinity, not can you represent infinity with a quantity of object.
3. Infinity is never used in any calculations, for counting, or for showing order in a series. Mostly because of aforementioned inability to actually represent anything tangible.

By your definition, infinity strikes out as number.
 
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