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  1.  
    Zero is odd and unfair
    •  
      CommentAuthorAngus
    • CommentTimeAug 3rd 2020 edited
     
    Zero is even as is well established. It is both an integer and a multiple of 2.
    The whole number system is unfair. It is particularly unfair when applied to money.
  2.  
    Money is imaginary and fair.
    •  
      CommentAuthorAngus
    • CommentTimeAug 3rd 2020
     
    Money is complex. Its imaginary part is probably fair.
  3.  
    there are 48 regular polyhedra
    https://www.youtube.com/watch?v=_hjRvZYkAgA
    •  
      CommentAuthorAngus
    • CommentTimeAug 5th 2020
     
    Wow!
    I'm inclined to seek a more restrictive definition of "regular polyhedron" for personal use.
  4.  
    As in "Would you like to come up to my pad and sort my polyhedra?"
  5.  
    What can we say about** the set of functions F such that
    F(a) + F(b) = F(ab) ?

    [[ Perhaps simpler is the set G such that
    G(a) + G(b) = G(a+b)
    because G(x) = k*x is one such function (linear).
    If G is the unitary function such that G(x) = x, then the relation is trivially always true. ]]

    If F is the unitary function such that F(x) = x, then this imposes the symmetric condition on a,b:
    a = b / (b-1)
    and (a-1)*(b-1) = 1.

    Anyway: do any F's exist which are true for all a,b? and if so, what are they?
    How the hell do you even begin to solve this?

    ** "Goes nicely with a piece of toast" is not acceptable
    •  
      CommentAuthorAngus
    • CommentTimeAug 14th 2020 edited
     
    You have to restrict that a bit otherwise you allow F(x)=0*x.

    Anyway Log[ a ]+Log[ b ]=Log[ab]

    That won't work if a or b=0, of course.
  6.  
    That's a great start anyway. Serious brainfart here.
    As far as that being the only function and who else belongs in the family? - no clue.
    •  
      CommentAuthorAngus
    • CommentTimeAug 14th 2020 edited
     
    It's also satisfied by Boolean NOT.
    NOT(a) OR NOT(b) = NOT(a AND b)
  7.  
    That's a fudge. OR is not AND.
    •  
      CommentAuthorAngus
    • CommentTimeAug 15th 2020 edited
     
    In Boolean logic OR can be represented "+" and AND represented "×". NOT is the "-" operator. Then syllogisms work if TRUE=1 and FALSE = 0. As you know well. So over the field of Boolean algebra (i.e 0 and 1) the proposition holds.
  8.  
    OK, that's right. But what a motley crew! - log, NOT...
    •  
      CommentAuthorAngus
    • CommentTimeAug 15th 2020
     
    Motley!! I am outrage!
  9.  
    •  
      CommentAuthoralsetalokin
    • CommentTimeAug 25th 2020 edited
     
    •  
      CommentAuthorAngus
    • CommentTimeAug 25th 2020
     
    Bifurcated.