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Infinity (1 Viewer)

kev-

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Why is (negative constant)^infinity undefined?
 

Sy123

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Because for a number:



That is the technical aspect of it.

Therefore if a is raised to a power of an undefined number (such as pronumeral variable x or infinity), then a must be greater than zero
 

deswa1

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Why is (negative constant)^infinity undefined?
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)?
 

Carrotsticks

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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':

 

mitchy_boy

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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':

lol that equals e, silly billy!
 

Sanjeet

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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?
 

Sy123

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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':

*Sketches graph on Geogebra and investigates*
*Sees asymptote*
mind=blown
 

Carrotsticks

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I 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.
 

mitchy_boy

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I 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.
my head almost exploded when my lecturer showed me this

i <3 maths

(that's why i'm do accounting)
 

SpiralFlex

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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':









































 
Last edited:

Carrotsticks

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Yep very nice. So many ways of proving that identity. A geometric way would be to use Upper and Lower Riemann sums for the ln(x) curve and to use the Squeeze Law (after a bit of re-arranging) very much like the 2009 HSC Q8(a).
 

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