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What's a number?

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

  1. Souron

    Souron The Dark Lord

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    What's a number, really? How do you define it? Are there more than one consistent definitions?

    I'm using number here to mean the thing that a numeral stands for.
     
  2. PeteAtoms

    PeteAtoms FormulaRandom

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    It's a symbol (visually and mentally) that represents quantity or magnitude.
    Useful to distinguish varying degrees of 'more' and 'less.'
     
  3. Earthling

    Earthling Chieftain

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    A person who listens to too much "grunge" music and is, emotionally, a barren wasteland.
     
  4. Souron

    Souron The Dark Lord

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    So I'm asking about the thing it stands for, not the numeral itself.

    You say a number is a quantity or a magnitude. What are those, and are they different?
     
  5. Formaldehyde

    Formaldehyde Both Fair And Balanced

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    Numbers can be very confusing. But most people seem to agree that one is the loneliest number that you'll ever do.


    Link to video.
     
  6. ParkCungHee

    ParkCungHee Chieftain

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    Some however, contend that two can be as sad as one.
     
  7. PeteAtoms

    PeteAtoms FormulaRandom

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    I didn't say number were quantity or magnitude, they just represent those ideas.

    Quantity and magnitude are measurements describing the physical universe and relationships between mass/energy within space. If you have two 'things,' a relationship exists between them and with the observer as well.

    If you have more apples than me, you would need a way to communicate how much more.

    NUMERICAL COGNITION
     
  8. Onionsoilder

    Onionsoilder Reaver

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    Quantity is an amount of something. Like 7 apples. There are 7 separate, distinct apples.

    Magnitude is more of a scale, I believe. Like a magnitude 3 earthquake. It's not three separate earthquakes, but one larger one.
     
  9. Souron

    Souron The Dark Lord

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    So all numbers are a ratio?

    You'll be happy to know that this forum has [wiki][/wiki] tags.
     
  10. Birdjaguar

    Birdjaguar Entangled Retired Moderator Supporter

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    At a high level they are a "convention", an agreed upon way of organizing things. In the beginning they were for counting and measuring.
     
  11. cardgame

    cardgame Sensual Kitten

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    RELEVANT - if only slightly.

     
  12. Perfection

    Perfection The Great Head.

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    Numbers have all sorts of amazing properties.

    For instance:

    There's one number that if you use on a telephone lets you speak to Perf! Many people have resorted to desperate measures in attempt to figure out what this number is.
     
  13. Souron

    Souron The Dark Lord

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    Numerals are conventions. But numbers, like all things in math, exist whether there is anyone around to use them or not. Right?
     
  14. azzaman333

    azzaman333 meh

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    Numbers are fun.
     
  15. suiraclaw

    suiraclaw Hell is other people

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    God made the natural numbers, all the rest is the work of man.
    - Leonard Kronecker

    More concrete answer: http://en.wikipedia.org/wiki/Peano_axioms

    edit: also relevant quote
    Numbers exist only in our minds. There is no physical entity that is number 1. If there were, 1 would be in a place of honor in some great museum of science, and past it would file a steady stream of mathematicians gazing at 1 in wonder and awe.
    - Linear Algebra by Fraleigh/Beauregard
     
  16. Tee Kay

    Tee Kay Just a passenger

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    No they're not.
     
  17. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    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.
     
  18. Souron

    Souron The Dark Lord

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    As Pete Atoms points out numbers are closely related to quantity and magnitude, which are physical properties, though not the kind of entities you can put in a museum.

    Also, the Peano axioms are only about natural numbers. How do you define the set of real numbers as an operation on the natural numbers?
     
  19. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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  20. Birdjaguar

    Birdjaguar Entangled Retired Moderator Supporter

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    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.
     

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