transfinites

Oology

translated by Michael Joseph Halm

It was in 1915 that P. E. B. Jourdain translated and so popularized Georg Cantor's work with transfinite cardinal numbers (such as aleph-null and aleph-one) and only in 1963 when B. S. Johnson defined the square root of aleph-one. In 1972 when John Horton Conway defined surreal numbers (see Mpossibilities 31:4), using the me mathematics changed. Many undefined terms suddenly were definable. The number of kinds of infinities increased more than infinitely.

Making use of the computerese (and roulette) 00 (double zero) for the first inaccessible number and the equally familiar computerese, \ (backslash), for ciscendentals, enfinities, enrationals, arrationals (Mpossibilities 68:1, neologisms) seems to make surreal mathematics easier by an aleph-nullth. [That's a word you probably don't see every day.]

Here're other surreals anglicized from Transfini Mathematiques pur Surreel Amateurs de Rôles Muet by André Joyce:

. . . 00.1 = 00 + .1 = 1\1 [read as "one conquered by one" (as opposed to "divided by" from phrase "divide and conquer"), or "one under one"]

. . . 001 = 00 + 1 = 10\1

. . . 002 = 00 + 2 = 5\1

. . . 003 = 00 + 3 = 10\3

. . . 012486374987513625012486374987513625 = 19\10

. . . 03193712565968062874340319371256596806287434 = 23\10

. . . 032967032967 = 13\10

. . . 06287434031937125659680628743403193712565968 = 23\20

. . . 329670329670 = 13\1

. . . 331 = (G(2, 00, 10) - 1)/3 -2 = 15\2

. . . 33 = (G(2, 00, 10) - 1)/3 = 3\1

. . . 335 = 3\1 + 2 = 15\8

. . . 337 = 3\1 + 4 = 15\11

. . . 967032967032 = 13\3

. . . 96806287434031937125659680628743403193712565 = 23\13

. . . 987513625012486374987513625012486374 = 19\9

2\2 = 2(00) + 0.2

4\4 = (2\2)(2\2) = G(2, 2, (2(00) + .2))

5\5 = 5(00) + 0.5

7\7 = 7)00) + 0.7

8\8 = (2\2)(2\2)(2\2) = G(2, 3, (2(00) + .2))

. . . 99001 = G(2, 10^00, 10) - 999 = ooduplexminim

. . . 99501 = G(2, 00, 10) - 499 = ooplexminid

. . . 9901 = G(2, 00, 10) - 99 = ooplexminic

. . . 9951 = G(2, 00, 10) - 49 = ooplexminil

. . . 991 = G(2, 00, 10) - 9 = ooplexminix

. . . 996 = G(2, 00, 10) - 4 = ooplexminiv

. . . 998 = G(2, 00, 10) - 2 = ooplexminij

. . . 99 = G(2, 00, 10) - 1 = 3\3 = ooplexmini

(00^2 + 1)/00 = garoopliperoo = infiniti [Steven John Robinson]

angelic numbers

(numbers ending in infinite number of zeroes)

100. . . 00 = 10^00 = ooplex

1000. . .00 = 10^10(00) = xooplex

10000. . .00 = 10^100(00) = cooplex

100000. . .00 = 10^1000(00) = mooplex

10^(10^00) = ooduplex

10^(10^(10^00)) = ootriplex

10^00^^2 = ooplexpleooplex

Beyond these are what might be called the archangelic numbers:

00^00 = 00^^2 = G(3, 2, 00) = oopleoo

00^^00 = G(3, 00, 00) = G(4, 2, 00) = aleph-one

(00^^00)^^(00^^00) = G(2, 4, 2, 00) = aleph-two

G(00, 4, 2, 00) = aleph-aleph-null

Even when we have reached

G(00, 00, 00, 00, 00, 00)

we are alas negligibly closer to ultimate infinity, the Most High W.

for more see Let Us Remember André Joyce


	index André Joyce Fan Club \| Dominissimo \| Googology \| Hierogonometry \| Jootsy Calculus \| links \| Laws \| Merology \| neologisms \| non-Najunamarian \| Pataphysics \| Sequences \| transfinites \| trazillion \| zerology Oology translated by Michael Joseph Halm copyright 1978-2004 Hierogamous Enterprises It was in 1915 that P. E. B. Jourdain translated and so popularized Georg Cantor's work with transfinite cardinal numbers (such as aleph-null and aleph-one) and only in 1963 when B. S. Johnson defined the square root of aleph-one. In 1972 when John Horton Conway defined surreal numbers (see Mpossibilities 31:4), using the me mathematics changed. Many undefined terms suddenly were definable. The number of kinds of infinities increased more than infinitely. Making use of the computerese (and roulette) 00 (double zero) for the first inaccessible number and the equally familiar computerese, \ (backslash), for ciscendentals, enfinities, enrationals, arrationals (Mpossibilities 68:1, neologisms) seems to make surreal mathematics easier by an aleph-nullth. [That's a word you probably don't see every day.] Here're other surreals anglicized from Transfini Mathematiques pur Surreel Amateurs de Rôles Muet by André Joyce: . . . 00.1 = 00 + .1 = 1\1 [read as "one conquered by one" (as opposed to "divided by" from phrase "divide and conquer"), or "one under one"] . . . 001 = 00 + 1 = 10\1 . . . 002 = 00 + 2 = 5\1 . . . 003 = 00 + 3 = 10\3 . . . 012486374987513625012486374987513625 = 19\10 . . . 03193712565968062874340319371256596806287434 = 23\10 . . . 032967032967 = 13\10 . . . 06287434031937125659680628743403193712565968 = 23\20 . . . 329670329670 = 13\1 . . . 331 = (G(2, 00, 10) - 1)/3 -2 = 15\2 . . . 33 = (G(2, 00, 10) - 1)/3 = 3\1 . . . 335 = 3\1 + 2 = 15\8 . . . 337 = 3\1 + 4 = 15\11 . . . 967032967032 = 13\3 . . . 96806287434031937125659680628743403193712565 = 23\13 . . . 987513625012486374987513625012486374 = 19\9 2\2 = 2(00) + 0.2 4\4 = (2\2)(2\2) = G(2, 2, (2(00) + .2)) 5\5 = 5(00) + 0.5 7\7 = 7)00) + 0.7 8\8 = (2\2)(2\2)(2\2) = G(2, 3, (2(00) + .2)) . . . 99001 = G(2, 10^00, 10) - 999 = ooduplexminim . . . 99501 = G(2, 00, 10) - 499 = ooplexminid . . . 9901 = G(2, 00, 10) - 99 = ooplexminic . . . 9951 = G(2, 00, 10) - 49 = ooplexminil . . . 991 = G(2, 00, 10) - 9 = ooplexminix . . . 996 = G(2, 00, 10) - 4 = ooplexminiv . . . 998 = G(2, 00, 10) - 2 = ooplexminij . . . 99 = G(2, 00, 10) - 1 = 3\3 = ooplexmini (00^2 + 1)/00 = garoopliperoo = infiniti [Steven John Robinson] angelic numbers (numbers ending in infinite number of zeroes) 100. . . 00 = 10^00 = ooplex 1000. . .00 = 10^10(00) = xooplex 10000. . .00 = 10^100(00) = cooplex 100000. . .00 = 10^1000(00) = mooplex 10^(10^00) = ooduplex 10^(10^(10^00)) = ootriplex 10^00^^2 = ooplexpleooplex Beyond these are what might be called the archangelic numbers: 00^00 = 00^^2 = G(3, 2, 00) = oopleoo 00^^00 = G(3, 00, 00) = G(4, 2, 00) = aleph-one (00^^00)^^(00^^00) = G(2, 4, 2, 00) = aleph-two G(00, 4, 2, 00) = aleph-aleph-null Even when we have reached G(00, 00, 00, 00, 00, 00) we are alas negligibly closer to ultimate infinity, the Most High W. for more see Let Us Remember André Joyce