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| ``Re: Equivalence of equations''
by Xtraeme on 2009-11-03 18:00:04 |
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| Good reply, Ivo. :)
Though I'd like to say that through my own informal analysis the multiplicative inverse of 0 is any given Real.
Consider if you take a circle and separate it into it's two constituent pieces(cosine and sine) and then set the two as a ratio of each other we form the tangent function (sine / cosine). Observing the convergence of the opposite to the adjacent over a single period (0 to pi) we see the tangent function goes from 0 to +complex infinity on the left of (pi / 2) to -negative complex infinity to 0 on the right. What this shows is that dividing by 0 or approaching nothingness pulls out all parts of all numbers over a single phase (which makes sense when viewed under the lens of Lim x->inf 1/x = 0 and heck it even makes sense in terms of the Heisenberg-uncertainty principle). No number is duplicated in the y (other than 0) along the single phase from 0 to pi. Yet amazingly all Reals are generated as these two waveforms converge towards and away from each other.
Maybe one day I'll have the insight to formalize why I see this to be the case. |
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