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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=b^{2}
SO, aba^{2}=b^{2}a^{2}
SO, a(ba)=(ba)(b+a)
So, a(ba)=(b+a)(ba)
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.)
Aryabhatta1 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=b^{2}
SO, aba^{2}=b^{2}a^{2}
SO, a(ba)=(ba)(b+a)
So, a(ba)=(b+a)(ba)
So, a=b+a
But, a=b
So, b=a
So, a=a+a
So, a=2a
So, 0=2aa
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
915 = 410
Adding 25/4 to both sides:
915+(25/4) = 410+(25/4 )
Changing the order
9+(25/4)15 = 4+(25/4)10
[This is just like : a square + b square  two a b = (ab)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
(35/2)(35/2) = (25/2)(25/2)
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!!
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