supramundane

[AntonioLao]

The mathematics of the supramundane is beyond boring. This boredom is meant to last forever as can be represented by rational numbers of repeating decimals. Some proper fraction examples are 1/9=.111111.. repeating 1’s, 2/9=.222222..repeating 2’s, 3/9=.333333..repeating 3’s, 4/9=.444444..repeating 4’s, 5/9=.555555..repeating 5’s, 6/9=.666666..repeating 6’s, 7/9=.777777..repeating 7’s, 8/9=.888888..repeating 8’s, 1/11=.090909..repeating 09’s, 2/11=.181818..repeating 18’s, 3/11=.272727..repeating 27’s, 4/11=.363636..repeating 36’s, 5/11=.454545..repeating 45’s, 6/11=.545454..repeating 54’s, 7/11=.636363..repeating 63’s, 8/11=.727272..repeating 72’s, 9/11=.818181..repeating 81’s. Surprisingly, there is no proper fraction which can give repeating decimals of .999999..repeating 9’s. However, for ��/(��+1) where �� is an increasing multiple factors of 10’s then the resulting decimal number would start with a series digits of 9’s followed by the same digits of 0’s. For examples, 10/11=.9090909.., 100/101=.99009900990099.., 1000/1001=.999000999000999000999…, 10000/10001=.99990000999900009999… 100000/100001=.9999900000999990000099999.., etc. On the other hand, the equivalent fractions of 1/9 is 11/99, 111/999, 1111/9999, 11111/99999, etc., 2/9=22/99=222/999=2222/9999=22222/99999, etc., 3/9=33/99=333/999=3333/9999=33333/99999, etc., 4/9=44/99=444/999=4444/9999=44444/99999, etc., 5/9=55/99=555/999=5555/9999=55555/99999, etc., 6/9=66/99=666/999=6666/9999=66666/99999, etc., 7/9=77/99=777/999=7777/9999=77777/99999, etc., 8/9=88/99=888/999=8888/9999=88888/99999, etc. Fortunately, Gottfried Leibniz (1646-1716) discovered that the transcendental irrational number �� can be expressed as the infinite series of alternating supramundane of sums and differences: ��=4({∑(1/��) where ��=5 stepping ��+2 as ��→∞}-{∑(1/��) where ��=3 stepping ��+2 as ��→∞}). Nonetheless, for �� equals infinite power of 10 then all repeating decimals including �� can be shifted by infinite power of 10 divisors with the supramundane rational number ��/(��+1) analogous to Cantor (1845-1918 ) transfinite numbers. See http://en.wikipedia.org/wiki/Leibniz_formula_for_pi and http://en.wikipedia.org/wiki/Georg_Cantor, http://en.wikipedia.org/wiki/Transfinite_number