azzaman333
meh
No they're not.
That's why you're not doing a maths/stats degree
No they're not.
Why stop at finite?I'd say a number is any finite quantity though. Then we can say i = sqrt(-1) is a number too![]()
wiki said: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,
Why stop at finite?![]()
Two objections here:A number is a mathematical object used to count and measure. Nothin else to it..
I don't buy it.Because finite quantities obey the usual rules of arithmetic (which ones depends on the numbers and operators involved of course)?
How's this any different from infinite numbers?Nah, it's just division by zero is ambiguous so undefined.
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.
Without a definition of quantity, all this is saying is that numbers are by definition finite. Which isn't saying much at all.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.
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.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.
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?
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.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.
Same story, what is an abstract object?An abstract object.
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.Why is it a mess, anyway? What's the controversy?
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.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)
If the honeycomb has mathematical relationships in it, then doesn't it have an existence independent of our mind?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.