Sunday, September 30, 2012

Incredible Division

In mathematics, especially in elementary arithmetic, division (÷) may seem as an arithmetic operation. But there is a philosophy behind division.

Most think division is one dimensional. The can easily get away with simple calculations, but get into trouble with sophistication

Example-1: 2 children ate 10 toffies, equally. How many toffies did each child eat?  5
a=10, b= 2, therefore, c=5

Note: children (b=2), toffies (a=10) and the answer (c=5) are in different dimensions.

Division basically deals with 3 dimensions/ scales, and also can expand up to 4 dimensions.

Division involves relativity, ratio and synthesis.

The answer (c or c/d) is the synthesis  of a relative to b.

a : b is the ratio.


Calculations - Nothing Vs. Anything

Set-A and Set-B may be in different sizes. (Think of a large bucket and a small bucket)
Let Set-A = 6; Set-B=3. Therefore, K=2

Irrespective of size, if the notion of completeness is considered, K=1

Suppose you came to fight Boxing game and your opponent does not appear. What would the result be?

Possibilities are:
1. No Game - You=0 , Opponent=0
2. Play & you win - You=1 , Opponent=0
3. Play & draw - You=1/2 , Opponent=1/2

Decision is based on consideration to another similar case (Set-c relative to Set-d, where Set-d=no appear).

The notion of Emptiness is same, irrespective of size of the container.

How many Emptiness are there in Emptiness?

To select from all possibilities, we refer to another similar case

Same as above.

Selecting a possibility is undecided until referring to another similar case.

Multiplication or Division with Emptiness/Nothingness is undefined unless a protocol is set.

Suppose millimeter sets,
  Set-E= from 1cm to 2cm= {0,1,....,9,10}mm
  Set-F= from 2cm to 3cm= {0,1,....,9,10}mm

 Set-E upper fence (10)=Set-F lower fence(0)

but, Set-E's everything (0->10) is not Set-F's nothing.(0->0)

Calculations - Infinity Vs. Infinitesimal

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