Awatmath.2344
net.math
utzoo!decvax!watmath!jagardner
Fri May 7 14:27:30 1982
Re: 2 = 1
Honestly, all this fuss over the 2=1 business!
Consider the line
x*x = x + x + x + x ... +x (x times)
Is this a function? Is there any other variable besides x?
This is merely an equation, so what are you differentiating?
It's like differentiating
x = 2
to get
1 = 0
Differentiation measures a rate of change in one thing in
comparison to another. If there is only one thing or if
there is no change (as in x=2), you can't just differentiate
using formulae learned by rote.
And while we're on the paradoxes, people should simply
realize that the square root function yields two values in
the complex plane (it does for real numbers too, but we
arbitrarily choose the positive square root as the *true* one).
The given paradox is just a fancier version of
(-3)**2 = 3**2
When you take square roots you get
-3 = 3 !
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