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Thread: Numbers are circular

  1. #1 Numbers are circular 
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    The definition of natural numbers starts with defining 0 as a number and the sucessor of a number is a number and then uses addition to define n+1 from n.

    But "sucessor of" translate into adittion of one and adition already assumes the numbers.


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  3. #2  
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    numbers need not have abstract definition as they come intuitively to us as a sentient species.

    even if we did not have a definition for the word three in our head we are able to identify the difference between nothing, a unit, a pair, a triplet, and other groups of objects. this is the concept often used to teach babies numbers using dots next to the arabic numbers that we normally use.


    physics: accurate, objective, boring
    chemistry: accurate if physics is accurate, slightly subjective, you can blow stuff up
    biology: accurate if chemistry is accurate, somewhat subjective, fascinating
    religion: accurate if people are always right, highly subjective, bewildering
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  4. #3 Re: Numbers are circular 
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    Quote Originally Posted by talanum1
    The definition of natural numbers starts with defining 0 as a number and the sucessor of a number is a number and then uses addition to define n+1 from n.

    But "sucessor of" translate into adittion of one and adition already assumes the numbers.
    Yep, the Peano Axioms basically the Natural Numbers and ordinary counting. So what ?


    "God made the integers, all else is the work of man." Leopold Kronecker
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  5. #4 Re: Numbers are circular 
    Your Mama! GiantEvil's Avatar
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    Quote Originally Posted by talanum1
    The definition of natural numbers starts with defining 0 as a number and the sucessor of a number is a number and then uses addition to define n+1 from n.

    But "sucessor of" translate into adittion of one and adition already assumes the numbers.
    http://en.wikipedia.org/wiki/Axiom
    Welcome to the wonderful world of axiom's.
    You will know when you meet one because;
    1: They are irreducible.
    2: They violate causality, having no predecessor.
    3: Without it(the axiom), nothing get's done.
    I was some of the mud that got to sit up and look around.
    Lucky me. Lucky mud.
    -Kurt Vonnegut Jr.-
    Cat's Cradle.
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  6. #5 Unsimplifiable Theorems are as Primes. 
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    You can use the computer and circular numbers to show unsimplifiable theorems are like prime numbers, simplifiable by other unsimplifiable theorems, to their simplest prime state. There is a sieve to find them, etc.
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