What is a paradox?

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Lets start with the easy stuff first. A paradox is an argument that produces a complete inconsistency within a logical common sense environment.

Many logical paradoxes are known to be invalid arguments as my fellow philosopher @kobiespriggs will attest, but these still hold value within critical thinking

OK let critical thinking commence ....

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Right, I'm going to think outside the box on this one for a start, so I'm going to use a mathematical paradox.

Lets look at the mathematical function:

f(x)=1xf(x)=1x with x∈[1,+∞)

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If we rotate this graph around the x-axis it creates a horn shaped 3D object called 'Gabriel's horn' (Yes as in the angel!).

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Using some second year University maths we can calculate the horn's volume and surface of the solid revolution and find ourselves something very paradoxical.

The solid has a volume of:

V=limt→∞π∫t1(1x)2dx=limt→∞π(1−1t)=π

and the surface:

S=limt→∞2π∫t11x1+1x4−−−−−√>S=limt→∞2π∫1t1x1+1x4>

limt→∞2π∫t1(1x)=limt→∞2πlnt=+∞

So, it appears that Gabriel's horn has an infinite surface, but only a finite volume. Very freaky!

For more on Gabriel's Horn, see Wikipedia at:

https://en.wikipedia.org/wiki/Gabriel%27s_Horn

@mindhunter

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P.S. Due to the Steemit formatting rules one mathematical symbol is missing - spot it and win 1 Steem!