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What's a number?

Discussion in 'Off-Topic' started by Souron, Apr 10, 2010.

  1. azzaman333

    azzaman333 meh

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

    Perfection The Great Head.

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    Why stop at finite? :confused:
     
  3. homeyg

    homeyg Deity

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    A number is a tune
     
  4. Lillefix

    Lillefix I'm serious. You can.

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

     
  5. warpus

    warpus In pork I trust

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

    ParadigmShifter Random Nonsense Generator

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    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.
     
  7. Perfection

    Perfection The Great Head.

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    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?

    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.
     
  8. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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

    Perfection The Great Head.

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    How's this any different from infinite numbers?

    (examples needed)
     
  10. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    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.
     
  11. Perfection

    Perfection The Great Head.

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

    ParadigmShifter Random Nonsense Generator

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  13. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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  14. Souron

    Souron The Dark Lord

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    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.
     
  15. Duo

    Duo Stay out of my territory.

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

    Souron The Dark Lord

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    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.
     
  17. warpus

    warpus In pork I trust

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    An abstract object.

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

    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)
     
  18. Birdjaguar

    Birdjaguar Hanafubuki Retired Moderator Supporter

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    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.
     
  19. Perfection

    Perfection The Great Head.

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    Same story, what is 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.

    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 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.
     
  20. Perfection

    Perfection The Great Head.

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

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