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Re: [Synoptic-L] Proof (?) that 222 was not written by Luke

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  • Emmanuel Fritsch
    ... Just because you apply a bad definition of is a part of as pointed out by Leonard just before. I do not know exactly if Leonard is or not a
    Message 1 of 26 , Feb 5, 2002
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      > >Strange things happen with negative numbers, I guess. The number -3
      > >also has the "parts" -4 and +1. Here, one part (-4) is -- on your
      > >student's reasoning -- smaller and the other (+1) larger.
      > >
      > Not merely on the student's reasoning, but on the definition of smaller
      > and greater laid down by the system of maths being used. The statement
      > -4 < -3 is true. It is true also that +1 > -3. Any number "to the left"
      > of another number on the number-line is smaller, by definition. And any
      > number "to the right" of another number on the number-line is greater,
      > by definition. This is not strange. It is normal. It does indeed follow
      > that, since -3 = -4 + 1, that the whole (-3) is greater than one of its
      > parts (-4) and smaller than another of its parts (+1), but that actually
      > confirms my point that the statement that the whole is greater than any
      > one of its parts is not even true, let alone self-evidently true.

      Just because you apply a bad definition of "is a part of" as
      pointed out by Leonard just before. I do not know exactly if
      Leonard is or not a mathematician, but I feel quite confident
      with his logic, first with the Goldbach conjecture, and now
      with the example of negative numbers.

      Leonard wrote :
      > When I said before that the subject and predicate have to be
      > clearly understood as a prerequisite for seeing the truth of a
      > self-evident proposition, I meant, among other things, the removal
      > of all such equivocities, and hence too, clarity regarding the question
      > of "what paradigm of thought is being used", as you describe it.

      The main equivocity is the use of set vocabulary in arithmetic.
      When you consider sets, for instance {1,2,a,b}, you may say it
      is greater than all its parts, for instance {1,b}.

      This property does not make sense when applied to arithmetic
      (or you should define the way to go from sets to arithmetic)

      a+
      manu

      PS : I know this is not the regular list to post this, and more over
      Leonard answered before almost all what would have been to said about.
      But I add one precision : the name of the property about even numbers
      expressed as sum of two prime numbers is called "Goldbach conjecture",
      and is known for more than three century, without having been demonstrated.
      Not really self evident.

      Synoptic-L Homepage: http://www.bham.ac.uk/theology/synoptic-l
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