Wednesday, February 18, 2015

Quantification of Infinities

Quantification of Infinities occurs as dimensions are involved.

On a one dimensional area, there is only X, however there are an infinite number of dimensions that X could occur in.

On a two dimensional plane, a shape is composed of angles. A circle can be seen as composed of one 360 degree angle, or an infinite number of 1/∞ degree angles.

When viewing a circle as an infinite number of angles. A sphere becomes more than infinite, each circle being composed of an infinite amount of angles, with each circle differing by 1/∞ degree, this creates an ∞^ ∞ number of angles.

This process repeats itself as dimensions are added, however the shapes cannot be comprehended by anything other than sets of numbers

A four dimensional sphere being defined by the coordinates +-1,+-1,+-1,+-1, this would continue the pattern, having ∞^ ∞^ ∞ number of angles.

Were one to attempt to argue that ∞^∞ is equal to ∞, the sphere becomes two dimensional, as it is lacking any angles in any plane besides that of the foundation circle.

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