Monday, March 18, 2013

Wonder Numbers: 0 , 1, ∞ and To Understand Division by grouping mechanisms


Wonder Numbers: 0 ,  1,  ∞

1.       NOTHING IS SOMETHING ?

Nothing is symbolized by 0.
Something is symbolized by 1 – the least value number.
i.e.  0 = 1 ?

Steps to prove the above statement:
1 + ∞  =  ∞  (Assumed) – on the assumption - even if you add any number to infinity, the resultant number will be infinity only. )
Then, 1 =  ∞ - ∞ = 0 ! 
Something is Nothing and Nothing is Something.
See the calculation below:
In 1 +  ∞  = ∞ + x , because some value is being added to infinity.
i.e. 1= ∞ + x – ∞ = ( ∞ - ∞ ) + x = 0 + x = x
Then 1 = x.
That proves that if we add a number to infinity, infinity also changes its value.
Hence 1 + ∞ = ∞ proves to be wrong, but, it should be ∞ plus.
Even the least value number say 1, adds value to the very large number i.e. infinity?

2.       Multiplication:
1.       Something multiplied by nothing becomes Nothing.
2.       Even infinity multiplied by nothing becomes Nothing.
Nothing becomes powerful compared to addition.
Example for item 1 above: 1 x 0 = 0
Example for item 2 above: ∞ x  0 = 0
3.       Division:
Nothing divided by something becomes Nothing.
Nothing divided by infinity also becomes Nothing.
But,
Something divided by Infinity becomes Infinity! – Perhaps valid argument to show the benefit of sharing by division.
Infinity divided by nothing becomes infinity.

O /  1  =  0     &     0 / ∞  =  0.
But,
1 / ∞ = ∞    &    ∞ / 0 = ∞.

Fallacy or wonder of maths:
To prove:
0 / 0  = 1 ?
Steps:
0 / 0 = 1  - assuming 0 as any other number like 1,2,3 et.  i.e. 3/3 = 1 and not 3. Hence 0/0 can be reasonably assumed to be 1 and not 0 on the above analogy. 
Take the equation:   0 / 0  =  1
i.e. 0 = 1 x 0 = 0
Hence, 0 / 0 = 1 is correct.

Let us apply the same principle to multiplication:
0 x 0 = 0
Divide by 0 the above equation.
0 x 0 / 0 = 0 / 0.
Applying our findings of 0/0 equals 1, the above will be: 0 x 1 = 1 i.e. 0 = 1 / 1.
i.e. 0 = 1?

To Understand Division by grouping  mechanisms

6 divided by 2 =  3.
Method:



 In the above there are two rows of 6 blocks. Because we have to divide 6 by 2.
Now, group these 12 blocks into 2 blocks each. Then again group them clubbing 2 together.
 

1 & 2 – group A
  

3 & 4 - group  B

5 & 6 – group  

7 & 8 – group  D

9 & 10 – group  E

11 & 12 – group F

Note: A & B one Group; C & D - another group; E & F - third group

You are having three groups and the answer is 3.

Now, 7 divided by 2 = 3.5

How to get it.



 Group the above block into blocks of two as above.
1 & 2 – Group A
3 & 4 – Group B


  


 

5 & 6 - Group C 
7 & 8 – Group D

9 & 10 - Group E 
11 & 12 – Group F

13 & 14 – Group G  - There is no matching block and is remainder block.

Then group them into two and again group into 2.
We have 3 fully matching blocks and one remainder block.
Hence answer is: 3.remainder block.
Now we have to find the value of remainder block. 
4 blocks mean one number and here we have 2 blocks – 13 and 14. Ie. Half. i.e. 0.5.
Hence the answer is: 3.5.