Absolute infinity

Absolute infinity is intended to serve as the supremum of all transfinite cardinals and ordinals. This idea has been proposed by Georg Cantor, and is denoted as ת or \(\Omega\). Cantor has linked this concept to the Abrahamic God.
The collection of all cardinals is denoted ת (tav), also by Cantor. ת cannot have a cardinality, because it would lead to the . 
Absolute infinity cannot be also treated as a set of all ordinals, \(\Omega\) for the same reason. Instead, it can be treated as the proper class of all ordinals, which is usually denoted by \(\textrm{Ord}\) or \(\textrm{On}\). Unlike absolute infinity itself, the class frequently appears in googology. For example, it is used in the transfinite induction and in the definition of Little Bigeddon.
Note that absolute infinity is a well-ordered class by itself if we identify it with \(\textrm{Ord}\). Every initial segment of it is an ordinal.
Sbiis Saibian stated himself that it is "not considered an official transfinite number" and "there is no such thing as a largest number". He denotes this by a red \(\color{red}{\Omega}\). However, the initial idea of absolute infinity by Sbiis Saibian was thinking about it as "the largest infinite number", which is paradoxical and thereby the term "absolute infinity" is not commonly used in the meaning of \(\textrm{Ord}\). In that case, it might be better to informally think about absolute infinity as some indefinitely large uncountable ordinal so that it is larger than any ordinal for which we can pick a reasonably large system of axioms in order to define it. Sbiis Saibian himself made a page showing that there are always larger "absolute infinities" in that sense.
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== See also ==
Category:Concepts
zh:绝对无穷
Category:Transfinite ordinals