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Fundamental mathematic proofs

  1. Nov 7, 2004 #1
    Fundamental mathematic proofs....

    I know this may seem a slightly odd question, but are there any website or pdf files, etc, floating around of proofs of the basic pricipals and "tricks" of maths? eg - adding, subtraction, multiplication, division, fractional sums and products, percentages, etc? I ask because I feel that these basic bits of maths are often over looked as we are simply told "this is how you do this" - are there any algebraic proofs for these?

    Thanks. :wink:
  2. jcsd
  3. Nov 7, 2004 #2


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    I highly doubt there are proofs of these operations. This is because they are the axioms upon which the modern mathematical structure was built upon. Somebody proved (I wish I could remember his name!!) using logic that axioms cannot be proved using themselves, and that given any set of axioms there will be some problems that are true but cannot be proven...by changing the axioms you change which problems can/cannot be proven.
    In short, they cannot be proven because they are the basic rules used to prove things. Don't worry-they aren't wrong. They are just the necessary assumptions we have made for centuries.
  4. Nov 7, 2004 #3
    His name was Godel.
  5. Nov 7, 2004 #4


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    We don't generally prove things like additon, we define them.
  6. Nov 7, 2004 #5


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    It depends, however, on what you are actually asking about:

    If you are asking:
    How can I prove the correctness of the procedure by which we convert a fraction of two naturals into the equivalent decimal representation of that fraction; then this is the same as asking for a proof of Euclid's algorithm which surely exist somewhere.

    It is also common in school to call this procedure "division".
  7. Nov 7, 2004 #6
    If I recall correctly there is a proof that 1+1=2. I remember seeing it, it was long and complex. I forget the exact name though, sorry.
  8. Nov 7, 2004 #7
    The proof is in Russell and Whitehead's Principia Mathematica and it is about 168 pages long. It derives 1+1=2 from the axioms of set theory.
  9. Nov 7, 2004 #8


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    These days, 2 is usually defined to be 1+1, so that proof is fairly short. :smile:
  10. Nov 9, 2004 #9
    It depends upon what you are asking. They are writers who will tell you about mental math, for example in the formula (X+1)^2 = X^2 +2X +1, this means that if you know 15^2, you can use the formula to find 16^2. Many such "tricks" exist.
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