1 = 2

[Safari]

I saw this one on another forum today:

Study => No Fail
No Study => Fail
Study + No Study => No Fail + Fail
Study(1+ No) => Fail (No + 1)
Study(No + 1) => Fail (No + 1)
We cansle (No + 1):
Study => Fail

Q.E.D

[MXP]

>>That's the problem. You can only split up an exponential in this way when using real numbers.

Why? It seems valid to me...

It's not valid for complex or imaginary numbers. This "proof" demonstrates that it is not valid since it gives an incorrect result.

[Alvaro]

The problem is that for positive real numbers we have a natural way of picking one of the square roots of a number: pick the positive one. That allows for the identity
sqrt(a/b) = sqrt(a)/sqrt(b)
However, that identity is not true for arbitrary complex numbers because there is no natural way of deciding which square root we are talking about. Case in point
sqrt(1/-1) = sqrt(1)/sqrt(-1)
is only true in a weak sense, since you have to pick which square root you are talking about in each case so the result is true.

[Beer Hunter]

Study => No Fail
No Study => Fail
Study + No Study => No Fail + Fail
Study(1+ No) => Fail (No + 1)
Study(No + 1) => Fail (No + 1)
We cansle (No + 1):
Study => Fail

Amusing, but the flaw in this argument is really easy to spot. It assumes that No is not equal to -1.

[The Insomniacs Dream]

I prefer this:

-1 = -1

-1/1 = 1/-1

sqrt(-1/1) = sqrt(1/-1)

sqrt(-1) / sqrt(1) = sqrt(1) / sqrt(-1)

i / 1 = 1 / i

i = -i

1 = -1

uhh....how are you getting -i = -1 ... i squared = -1

[Wizard]

if you are refering to

Code: Select all

i = -i

1 = -1

just devide both sides by i.

[The Insomniacs Dream]

ah, i see...wasent thinking that way