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The Small Ignorance Ordinal (denoted as ♁) is the limit of any form of Numerical Array Notation using finite entries, and is considered to be the []-



functional equivalent of the Small Veblen Ordinal, of which this number is named after. Because of NAN's recent invention, numbers beyond Axiomatic Limit are not only possible, but now easily made because of a generalisation of []-functional ignorance level into a Veblen-like function.

Numerical Array Notation[]

Numerical Array Notation is a Veblen-like function created by Goodels as a way to generalize []-functional ignorant and axiomatic chains and create numbers much larger than even Axiomatic Limit. It is denoted as [a:b], which is beyond all "a" with ignorance level "b".

One can do [a:1,0] which has an ignorance level beyond all [a:b]. [a:1,b+1] is one ignorance level higher than [a:1,b]. Then we have [a:2,0] which is beyond all [a:1,b]. Then [a:1,0,0] which is beyond all [a:b,c] and [a:1,0,0,0] which is beyond all [a:b,c,d], and so on.

In the NAN hierarchy, A 0 is defined as [num:1, 0]. This can then be extended into B0 being [num:2, 0], C0 being [num:3, 0], and so on and so forth. Already, Axiomatic Limit can be compared as the NAN equivalent of the Feferman-Schutte Ordinal, also known as the limit of 2-entry NAN arrays, denoted as [num:1,0,0].

Definition[]

The Small Ignorance Ordinal is defined, just like the Small Veblen Ordinal, as the limit of any form of finite-entry NAN arrays. However, as the name suggests, a Large Ignorance Ordinal exists and is much, much larger than even this number...

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