Concept of discrete world

  1. There is finite discrete world
  2. World consists from objects
  3. Every object is atomic or contains other objects
  4. Every object is unique, that means:
  5. No one part of object is shared with some other object
  6. No object or its part contains itself (also in transitive manner)
  7. World exists finite amount of time
  8. Time consists from discrete clock ticks
  9. Something could happen only at some clock tick
  10. 'Something' is world state change: one object or one from its parts are created or removed

System concept

  1. System consists from two parts: world and computer
  2. Computer have fixed collection of laws describing possible state transitions
  3. Laws are permitting only one transition per tick
  4. World state change is happening only when laws are not violated.

Laws language

  1. Rules that describe initial world state
  2. Rules that describe state transitions
  3. Every object have a reason to exist: by rule application or as a part of an initial state

The code

$$ \frac{n!}{k!(n-k)!} = \binom{n}{k} $$

is rendered as the formula

n!k!(nk)!=(nk)\frac{n!}{k!(n-k)!} = \binom{n}{k}