Wiki Googologie
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Wiki Googologie

En googologie, les classes sont une façon de regrouper les nombres réels positifs par grandeur.[1] Inventé par Robert Munafo, le système est inspiré de la façon dont les humains perçoivent les tailles des groupes d'objets. De manière concise, les nombres de classe 0 sont ceux supérieurs ou égaux à 0 et inférieurs à 6, et les nombres de classe n sont les nombres dont les logarithmes en base 10 sont dans la classe n-1. Les superclasses utilisent le même concept mais avec une exécution différente.

Numéros de classe 0

Les nombres de classe 0 sont ceux qui sont si simples qu'ils peuvent être facilement reconnus en très peu de temps. Pour la plupart des humains, ces nombres vont de 1 à 6.

Numéros de classe 1

Class-1 numbers are small enough to be possible to perceive as a group of objects, but are larger than class-0 numbers. In other words, if x is a class-1 number, it is possible to see x objects in a single scene. Class-1 numbers range from 6 to 106 (one million), as it is difficult, but not impossible, to see a million objects in a single scene.

Numéros de classe 2

Class-2 numbers are small enough to be able to be exactly represented in decimal form, but are larger than class-1 numbers. Class-2 numbers begin at to (known as a maximusmillion or millionplex). This is simply a continuation of the pattern that can be seen in the relationship between class-0 and -1 numbers: the logarithm of a class-x number can be represented as a class-(x - 1) number. Googol, therefore, is a number in this class, as 101 digits can be represented in decimal form.

Numéros de classe 3

Class-3 numbers can be approximately represented in scientific notation. They range from to (known as a millionduplex), following the patterns of classes 0, 1, 2, and 3. Googolplex is a class-3 number.

When represented as a power tower in a computer, a class-3 number x is practically indistinguishable from x + 1.

Numéros de classe 4

Class-4 numbers have class-3 base-10 logarithms. They range from to .

When represented as a power tower in a computer, a class-4 number x is practically indistinguishable from 2x.

Classes supérieures

Class-5 numbers have class-4 base-10 logarithms. They range from to .

In general, class-n numbers are those numbers that are larger than class-n-1 numbers, and whose have class-n-1 base-10 logarithms. By using the notation hyper-E, the upperbound of the class-n number is E6#n.

Références

  1. Large Numbers, Robert Munafo
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