Axiomatic Limit (⏁) is defined as the limit of []α functions (where α can be replaced with any number, even other []α functions) defined in the A_0
article. In there, A0 is defined as the number larger than all counting numbers, and ignores all axioms and paradoxes which state it is not the largest counting number. This makes it exceptionally hard to advance any further than A0, however due to A0's nature of ignoring axioms that go against it's existence, one can generalize the property into an infinite chain of axiomatic and paradoxical ignorance, with numbers such as A1 ignoring all axioms and paradoxes that go against it's own existence, therefore rendering A0 functionally non-existent to A1.
Definition[]
The nature of A0, as stated earlier, is that it is the number that surpasses all "counting numbers" and ignores all paradoxes and axioms that go against it's existence. This can be turned into an infinite chain of axiomatic and paradoxical ignorance, with obvious logical extensions such as AΩ and Aθ, along with the recursions of AA_0 and so on without any arbitrary endpoints. Immediately, we can already define a limit number for Aα functions where it is already larger than even infinite recursions of A-functions. This limit number will henceforth be defined as B0 (not to be confused with Outerconst).
As such, this can be generalized into yet another infinite chain of []-functions, each completely ignoring the axioms and paradoxes lower []-functions depend on. We can then define the set of all []-functions as ⩈.
The logical statement then follows that ⏁ ⩈> ⩈ (Axiomatic Limit is []-functionally beyond the set of all []-functions), therefore rendering ⏁ fully inaccessible to all forms of []-functions.