# Absolute Infinite

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The Absolute Infinite is mathematician Georg Cantor's concept of an "infinity" that transcended the transfinite numbers. Cantor equated the Absolute Infinite with God.[1] He held that the Absolute Infinite had various mathematical properties, including that every property of the Absolute Infinite is also held by some smaller object[citation needed].

## Contents

### Cantor's view

Cantor is quoted as saying:

Cantor also mentioned the idea in his letters to Richard Dedekind (text in square brackets not present in original):[5]

A multiplicity is called well-ordered if it fulfills the condition that every sub-multiplicity has a first element; such a multiplicity I call for short a "sequence".

...

Now I envisage the system of all [ordinal] numbers and denote it Ω.

...

The system Ω in its natural ordering according to magnitude is a "sequence".
Now let us adjoin 0 as an additional element to this sequence, and place it, obviously, in the first position; then we obtain a sequence Ω′:

0, 1, 2, 3, ... ω0, ω0+1, ..., γ, ...
of which one can readily convince oneself that every number γ occurring in it is the type [i.e., order-type] of the sequence of all its preceding elements (including 0). (The sequence Ω has this property first for ω0+1. [ω0+1 should be ω0.])

Now Ω′ (and therefore also Ω) cannot be a consistent multiplicity. For if Ω′ were consistent, then as a well-ordered set, a number δ would correspond to it which would be greater than all numbers of the system Ω; the number δ, however, also belongs to the system Ω, because it comprises all numbers. Thus δ would be greater than δ, which is a contradiction. Therefore:

The system Ω of all [ordinal] numbers is an inconsistent, absolutely infinite multiplicity.