What's a number?

[azzaman333]

No they're not.

That's why you're not doing a maths/stats degree

 

[Perfection]

I'd say a number is any finite quantity though. Then we can say i = sqrt(-1) is a number too

Why stop at finite?

 

[homeyg]

A number is a tune

 

[Lillefix]

Ayone heard of Graham's number? I'ts big...

Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies at least one Planck volume. Even power towers of the form a^b^c... are useless for this purpose,

 

[warpus]

A number is a mathematical object used to count and measure. Nothin else to it..

 

[ParadigmShifter]

Why stop at finite?

Because finite quantities obey the usual rules of arithmetic (which ones depends on the numbers and operators involved of course)? I know hyperreal numbers have ordinals and infinitessimals though.

 

[Perfection]

A number is a mathematical object used to count and measure. Nothin else to it..

Two objections here:
1. Calling it a mathematical object is simply sweeping a whole lot of the mess under a rug! What the hell is a mathematical object?

2. Your definition seems wrong. For instance how are complex numbers used to count?

Because finite quantities obey the usual rules of arithmetic (which ones depends on the numbers and operators involved of course)?

I don't buy it.

A real number can be divided by any real number except zero. Should we call zero not a number?

I don't think we can discount the idea of infinite numbers simply because they have special arithmetic properties.

 

[ParadigmShifter]

Nah, it's just division by zero is ambiguous so undefined.

 

[Perfection]

Nah, it's just division by zero is ambiguous so undefined.

How's this any different from infinite numbers?

(examples needed)

 

[ParadigmShifter]

I don't consider infinity to be a number.

Bump my maths thread though if you want to discuss further. I'm probably too drunk now.

 

[Perfection]

You can never be too drunk for math! I'm completely hammered at the moment.

 

[ParadigmShifter]

Well, have a read about hyperreal numbers then.

http://en.wikipedia.org/wiki/Hyperreal_number

We can discuss after I wake up tomorrow

 

[ParadigmShifter]

I mean surreal numbers, sorry

http://en.wikipedia.org/wiki/Surreal_number

 

[Souron]

http://en.wikipedia.org/wiki/Construction_of_the_real_numbers

Well there is a construction from integers in that list, but it still seems a bold claim to say that that's what makes real numbers numbers.

Peano is a good place to start.

I'd say a number is any finite quantity though. Then we can say i = sqrt(-1) is a number too

Then you can start classifying what properties your numbers satisfy.

Without a definition of quantity, all this is saying is that numbers are by definition finite. Which isn't saying much at all.

 

[Duo]

numbers are just a way of talking about things, just like "blue" or "above".

 

[Souron]

Numerals and nomenclature certainly are conventions. I'm not sure how you define numbers (assigned values?), so I'll hold off a bit on that part. Now "all things math" are relationships between assigned values. Math is an agreed upon language that expresses a relationship so we can understand/use that relationship. I would say that the relationships do exists independent of any expression we make of them. Birds fly all by themselves; they do not need nor do their brains use any mathematics to do so. Math is our way of expressing natural events. math does not exist out side of our brains.

I don't think I agree. Mathematical constructs exist whether there are people to think about them or not. A square was no less a square, before there were people. Math is not unique to people.

 

[warpus]

Two objections here:
1. Calling it a mathematical object is simply sweeping a whole lot of the mess under a rug! What the hell is a mathematical object?

An abstract object.

Why is it a mess, anyway? What's the controversy?

2. Your definition seems wrong. For instance how are complex numbers used to count?

You can use imaginary numbers to solve some cubic equations (and other polynomial equations), which in turn allows you to measure/quantify solutions to problems. (I did say measure or count)

 

[Birdjaguar]

I don't think I agree. Mathematical constructs exist whether there are people to think about them or not. A square was no less a square, before there were people. Math is not unique to people.

People created all math and we have the ability to see it in lots of places, but without our constructs, it doesn't exist. We created the idea of a square and its various relationships; those relationships are only meaningful to us. Bees build honey combs, but we see the mathematical relationships, bees don't.

 

[Perfection]

An abstract object.

Same story, what is an abstract object?

Why is it a mess, anyway? What's the controversy?

Numbers are very unusual things. We describe certain numbers existing and not existing (even prime number greater than two for instance), and give them all sorts of properties.

So what is the nature of this existence? We could say that they exist in terms of concepts, but if I can conceive of what even prime number greater than two might be like why doesn't it exist? We might argue that maybe numbers have some sort of special existence outside of concepts, but then where do they exist and how do we get to know them?

There are all sorts of interesting philosophical puzzles about the exact nature of numbers.

You can use imaginary numbers to solve some cubic equations (and other polynomial equations), which in turn allows you to measure/quantify solutions to problems. (I did say measure or count)

You said measure AND count. However, let's use your new definition of "measure or count". You certainly use the addition operator to measure (try solving cubic questions without that!) but they aren't numbers.

 

[Perfection]

People created all math and we have the ability to see it in lots of places, but without our constructs, it doesn't exist. We created the idea of a square and its various relationships; those relationships are only meaningful to us. Bees build honey combs, but we see the mathematical relationships, bees don't.

If the honeycomb has mathematical relationships in it, then doesn't it have an existence independent of our mind?