Friday, 5 June 2015

Reps and natural addition

Bony woman holding up feline mask, a writing: the natural

The key to success in creating big numbers is repetition: the rep. We repeat number variables x and words X in various ways. A word is a sequence of characters.

Listing examples of the rep notations we use.

  • a..
    some finite series of added a
  • Wa.. :n3 = WaWaWa.Wa.. :n
    rep of word W and variable a
  • a*b = a.. :b
    multiply, rep a times b, by natural addition, e.g.
    2*3 = 11*3 = 11+11+11 = 111111 = 6
  • (X){3} = X{3} = XXX
    = X{2}{2} = X{2}X{1}
    word group, regex quantifier, left associative.
  • E(2,4) = E(2+E(2,3))
    == E(2+..E(2,1)..) :3:
    = E(2+..E(2)..) :3:
    = E(2+..2..) :3:
    = E(2+..22..) :2:
    == 2222
    = 11111111 = 8
    function steps for the multiplication 2*4, known as 4×2
    using double reps, from outside to the middle.
  • 1... = ω
    units one, no halt, counts to infinity

Rep of numbers is repeated addition. Units 1 and in general any number of units, naturally add up by removing the plus + in between. Variables ab and numbers 22=4 are coloured green here, when they are already appended.

Repeat the negative unit - to create the negative numbers -{n} = -*n
Or append it to count off n- natural numbers.
The result when we add 1- is naturally empty. We let 0 denote an empty entry.

Numerical expressions in other formats, such as the decimal numbers, usually don't add up by appending them. For number variables natural addition always works.
The plus a+b is a temporary lock on addition, for people to do work on formatting numbers. Feeble colleagues who write mc2 to express multiplication c*c*m are by nature physicists. Their pretence is a dishonour to the mathematical profe$$ion. And the little ones 11 suffer.


The key to success in life is repetition too. Got a good idea? Tell others to repeat it! Learn how to overcome difficulty and apply it again and again.
      Mother nature codes all information in our DNA and organisms that behave wrongly – working all night on their anarchistic scheming – will lose opportunities to share their genetic code and perish as a result. Don't let this happen!

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