Math sure is fun

29 01 2010

With years of looking into the math and learning the same 10 digits in various combinations possible, its comes to a point that , what we know is the only solution and if it does not fall into what we know as the concepts its not supposed to be a possible. Here are few solution that makes one enjoy the possibility of math and the fun in it.. Starts with the basics of math and ends with a solution thats not supposed to make sense.

1.

Proof for 1 = 0 or actually 2 = 0.

Lets take two variables a and b with values = 1.

a = 1
b = 1

a = b
a2 = b2
a2 – b2 = 0
(a-b)(a+b) = 0
(a-b)(a+b)/(a-b) = 0/(a-b)
1(a+b) = 0
(a+b) = 0
1 + 1 = 0
2 = 0

2.

Now to prove 2 = 1.

-2 = -2
4 – 6 = 1 – 3
4 – 6 + 9/4 = 1 – 3 + 9/4
(2 – 3/2)2 = (1 – 3/2)2
2 – 3/2 = 1 – 3/2
2 = 1

Two solutions which contradict the basics of math we have learnt till date. and also they contradict each other. With some googling found out that the first solution has a flaw when we try to divide the number by zero(a-b)  which is not allowed. The second solution , taking square roots always provides with a pair of values , + and – . since we are taking only the positive values the result is confusing.

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