Look at it like this. (-x)^2 is positive. (-x)^3 is negative. In general, (-x)^2n is positive whilst (-x)^2n+1 is negative. The reason it is undefined is because of the fact that is infinity even (therefore (-x)^infinity is positive) or odd (negative)?Why is (negative constant)^infinity undefined?
lol that equals e, silly billy!Actually, any number (positive or negative) to the power of infinity is undefined.
Even 1 to the power of infinity is undefined (people think it's still 1).
Tell me what you think about this 'proof':
Seems right to me, can you explain a bit more?Actually, any number (positive or negative) to the power of infinity is undefined.
Even 1 to the power of infinity is undefined (people think it's still 1).
Tell me what you think about this 'proof':
Haha how can that be!? 1 to the power of infinity is ~obviously~ equal to 1 =plol that equals e, silly billy!
*Sketches graph on Geogebra and investigates*Actually, any number (positive or negative) to the power of infinity is undefined.
Even 1 to the power of infinity is undefined (people think it's still 1).
Tell me what you think about this 'proof':
did you know l'hospital STOLE that from his mate, and he didn't actually think it up himself...L'Hopital's Rule
Yes. Someone told me that but not sure if I should accept it.did you know l'hospital STOLE that from his mate, and he didn't actually think it up himself...
it's true
you definitely shouldYes. Someone told me that but not sure if I should accept it.
my head almost exploded when my lecturer showed me thisI remember seanieg89 saying something really funny before... something along the lines of:
"What is 1 to the power of chair?"
to prove his point.
Essentially, infinity isn't a number and can't be treated as such. Anything dealing with infinitismals is VERY sensitive.
ie: Consider an infinite series. If it is 'Conditionally Convergent', I can actually make it converge to ANY value I want it to with a specific permutation of the terms. But it is a permutation of INFINITE terms. This is called Riemann's Arrangement Theorem.
You can even make it diverge! A classic example of this is that by manipulating the Alternating Harmonic Series (which converges to ln2), we can make it converge to say 3/2 ln(2), which is most certainly false.
Actually, any number (positive or negative) to the power of infinity is undefined.
Even 1 to the power of infinity is undefined (people think it's still 1).
Tell me what you think about this 'proof':