Saturday, 1 June 2013

More odd maths

Bear with me on this one...

If you divide A by B and then times the result by B you end up back at A.  Same score if you times first and then divide.

(AxB) ÷ B = A

(A÷B) x B = A

You can do the same with plus and minus.

A - B + B = A

A + B - B + A

At this point I'm plugging Swedish pop music, so I'm going to swap out the B for an altogether bigger number: ∞, or infinity.  Now if you divide a number by infinity then the resultant fragments of that number are infinitely small (1x10^-∞), but there are an infinite number of them.  Recombining an infinite number of any number, however small, results in infinity.

A ÷ ∞ x ∞ = ∞, not A!

A x ∞ ÷ ∞ = ?

If ∞ is divided by ∞, do we get ∞ or 1?  Either way, unless A = 1 we don't end up back at A.

Now addition.  A + ∞ = ∞.  Playground hyperbole notwithstanding, there is no such number as infinity plus a thousand.

A - ∞ + ∞ = ∞

A + ∞ - ∞ = ?

Again, if infinity is subtracted from infinity then we end up with either infinity or nothing, depending who you ask.  The point is this:

if A ÷ B x B = A,

and A ÷ ∞ x ∞ = ∞,

then A = ∞!  All numbers, following this mathematical quirk, equal zero, one, and infinity, all at the same time!  Small wonder those three numbers are so special in maths.  All numbers are infinite and all numbers are nothing, rendering maths both fundamentally important and fundamentally impossible all at once.  The universe and nature all run on the power of numbers, but the numbers themselves are irrelevant at this level.  They exist and yet do not exist.

This would be a fabulous time to experiment with LSD.

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