My Notebook

Pursuit of Clarity.

Mathematics-1

Lets tracking a sytem:

  • We are unable to track a system because we don’t have notion of Identity.
  • Once we have gave the Identity to a object in a system, then problem is solved.
  • Constraint:-Finite memory of the Manager (manging arbitary identity symbol)
  • To manage memory efficiently:-
    • grouping in homogenous way. Heterogenous would be difficult
    • Need to store symbol, and track symbol by symbol
    • .
    • Need someway to represent the identity symbol in a compact way

Approach-n:(Need someway to represent the identity symbol in a compact way)

  • Finally we decided some kind of cyclic symbol is needed and their order will be important for us. And also which cycle it belongs is also important
Representation of Cyclic Structure of symbol
1
2
3
4
5

  i k l
  ii ik il
  ki kk kl
  li lk ll
  .......

So Finally Identity problem is on our track.

Operation

  • Operration on symbol introduce neew symbol.

    • Subtraction: Introduce “SUNYA” and reflection of a symbol on other side.
    • Division: Introducing fration symbol
    • SQUARE ROOR: Introduce root(n)
    • .
    • .

  • Grouping of Symbol by underdestanding properties of symbol.

Note: new symbols are introduced, when new operation are added to system.

Algebra:

  • Concept of container/variable: which can take any value with their domain.
  • Concept of “equal to”/“same as”. equality/operation only hold on same types of object.

References:-