I saw this and thought of you people, for some reason.
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So I went and found this on a page of math "humor", in particular
of bogus proofs. This one ain't bad; a nice variant to a classic.
The aim is to prove that 1 = 2.
Notice the following:
1 = 1^1 = 1
2 + 2 = 2^2 = 4
3 + 3 + 3 = 3^2 = 9
4 + 4 + 4 + 4 = 4^2 = 16
and in general:
x + x + ..... + x = x^2
\___ x times ___/
Derive in place:
1 + 1 + ..... + 1 = 2 x
\___ x times ___/
1 * x = 2 x
Simplify by x which is not zero, 1 = 2.
Note the formula is valid for pure fractionals too, for example:
0.05 + 0.05 + 0.05 + 0.05 + 0.05 =
0.01 * (5 + 5 + 5 + 5 + 5) = 0.01 * 5^2 = 0.05 ^2 = 0.25
and thus it is valid for any real number x because we can always write x as
a sum of a pure integer u and a pure fractional v: x = u+v. For example
x=3.8 => u=3 and v=0.8. So we are not deriving in a discrete space, think
somewhere else.
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--
real minaret
