i²= 1 (cross-multiplication)
How to solve this paradox?
I also don't know the answer.
Last edited by wcy (2005-08-07 01:42:27)
I've already discussed that on IRC and nobody could explain that too..
i suspect that it is illegal to square root both sides, since square rooting a negative number is not allowed
"How wonderful that we have met with a paradox. Now we have some hope of making progress." - Niels Bohr
I suspect it is this curious phenomenon:
(-1)² = 1²
-1 = 1 ...?
i/1 = 1/i ...?
1/i = (1 x i) / (i x i) = i/i² = i / -1 = -i
* basks in glow of very rare victory, hoping it lasts *
Normally, in such paradoxes, this is where the mistake lies.
Since a² = b²,
it cannot be inferred that a=b.
Taking square root on both sides of an equation should always have the
'±' sign, after the square root is worked out.
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.