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Last edited by The_Shooman (2013-05-30 03:47:13)
It is represented in the maths. Each slice of cake contains all possible fractions of that 100%. They're all there.
Same with the straight number. That thing you think is left over is there in the fractions. It just keeps being chopped into 3 forever. Infinitely.
No, I think Shooey is on to something: ever tried to cut a cake into three equal pieces? Someone always gets a smaller piece.
It is for the person who gets the smallest slice of the cake!
Are we taking into account the globs of frosting and crumbs that stick to the knife when cutting a cake?
Liam and Formby are speaking truth, Shooey. If you don't believe them, watch this video, featuring a slightly porcine looking young lady who apparently doesn't know the word 'infinity'.
http://www.virtualnerd.com/middle-math/number-theory-fractions/fractions-decimals/repeating-decimal-definition
Shooey has a point actually. Consider infinities - there are an infinite number of infinities and some are considerably bigger than others. For example take the infinite set of real natural numbers i.e. 1,2,3,4, etc. then ponder the infinite set of real prime numbers 2, 3, 5, 7, 11 etc. The latter set is clearly smaller than the first set as it is an isolated sequence of selected natural numbers with a specific property. However both sets are infinite. Some infinities are bigger than others.
Not good enough?
OK, the fractal coastline conundrum. The length of a crenellated surface increases with accuracy of measurement. An object a foot long measured with a ruler can be calculated to be ten feet long if measured with a finer gauge instrument. The same object can be an infinite length if every single dimple no matter how minute is taken into consideration.
Mathematics may not contain the Devil but they probably contain God - He's just a number we cannot calculate yet. Something that will make Graham's number seem a mere blip........
Let's all meet at the bar at Hilbert's Grand Hotel and discuss this further.
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