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 Some astounding maths facts

There are many questions on how things works, how they occour....
Here, some of them would be solved.

1. Prove 1=2

A. Suppose a=b

So, ab=b2
SO, ab-a2=b2-a2
SO, a(b-a)=(b-a)(b+a)

So, a(b-a)=(b+a)(b-a)
So, a=b+a
But, a=b
So, b=a
So, a=a+a
So, a=2a
So, 1=2
Hence proved.

2. To find 'n' in the arithmatic progression(A.P.)
Aryabhatta-1 gave the formula to find the value of  number of term in A.P. But, I shortened it to:
((l - a)/d)+1
where, l = given last term, a= first term and d= difference between two terms.
If, a and d are same then 'n' can be found by :
l/d
where, l= given last term and d= difference between two terms.

3. To prove  0=any number.
A. Suppose a=b

So, ab=b2
SO, ab-a2=b2-a2
SO, a(b-a)=(b-a)(b+a)

So, a(b-a)=(b+a)(b-a)
So, a=b+a
But, a=b
So, b=a
So, a=a+a
So, a=2a
So, 0=2a-a
So, 0=a.
Here, a can be any number. So, 0=any number is proved to be true.

4. 3=2

Can any one prove 3=2. I hope none. But Ramanujam had.

See this illustration:

-6 = -6

9-15 = 4-10

9-15+(25/4) = 4-10+(25/4 )

Changing the order

9+(25/4)-15 = 4+(25/4)-10

[This is just like : a square + b square - two a b = (a-b)square.]

Here a = 3, b=5/2 for L.H.S....... and a =2, b=5/2 for R.H.S.

So it can be expressed as follows

(3-5/2)(3-5/2) = (2-5/2)(2-5/2)

Taking positive square root on both sides.

3 - 5/2 = 2 - 5/2

3 = 2

5. To prove 1=any number
Let 'a' be any number.
So, a * 0 = 0.
So, a = 0 / 0.
But, value of '0' is not known. So, let value of '0' be 'x'.
So, a = x / x
So, a=1.
Hence proved.

6. To prove 1 = 0.
Now, 0 = any number (see proof no. 3)
and, 1= any number (see proof no. 5)
So, 1 = 0.
Hence proved.

7. To prove negative integer = positive integer.
0 = any number (see proof no. 3)
So, 0 = a                                  (Here, 'a' is short form of 'any
number')
So,  (-a) = 0.                    (Tanking 'a' on other side)
Also, 0 = 0.
So, (-a) = 0 = a.
So, (-a) = a.
Hence, negative integer =positive integer.
Hence proved.

Can u find any flaws??

how was that??cool isn't it!!