Classe

En googologie, les classes sont une façon de regrouper les nombres réels positifs par grandeur. 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 $10^6$ to $10^{10^6}$ (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 $10^{10^6}$ to $10^{10^{10^{6}}}$ (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 $10^{10^{10^{6}}}$ to $10^{10^{10^{10^{6}}}}$.

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 $10^{10^{10^{10^{6}}}}$ to $10^{10^{10^{10^{10^{6}}}}}$.

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.