He labeled their cardinalities ℵ₀ (aleph naught) and ℵ₁ (aleph one), respectively, the first two “orders of infinity”, both smaller than absolute infinity Ω. In the Greek number system, it was taken as the symbol of 800. Just look at the 0=1 cardinal. This value is defined solely by the property BAI > n. This causes an ill-definition, as there isn't enough information to define BAI as something. If you use ZF set theory (with or without the Axiom of Choice), you can for any infinite cardinal construct one which is … And the symbol $\infty$ is a lemniscate which is used as an infinity symbol in a variety of contexts such as Calculus. The capital omega … This is the limit, unlike CAI. Omega Symbol in Greek Alphabet (Ohm Symbol) Omega (uppercase Ω, lowercase: ω) is the 24th and last letter of the Greek alphabet. Googology-testing Wiki is a FANDOM Games Community. The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. Class (set theory), Ordinals, ordinal analysis, and set theory, Double exponentiated polynomial omega level, Triple exponentiated polynomial omega level, Ackermann's Generalized Exponential Notation, Joyce's More Generalized Exponential Notation, $$\psi_0(\Omega^{\Omega^\omega})$$ (small Veblen ordinal), $$\psi_0(\Omega^{\Omega^\Omega})$$ (large Veblen ordinal), $$\psi_0(\varepsilon_{\Omega + 1}) = \psi_0(\Omega_2)$$ (Bachmann-Howard ordinal), $$\psi_0(\Omega_\omega)$$ with respect to Buchholz's ψ, $$\psi_0(\varepsilon_{\Omega_\omega + 1})$$ (Takeuti-Feferman-Buchholz ordinal), $$\psi_0(\Omega_{\Omega_{\cdot_{\cdot_{\cdot}}}})$$ (countable limit of Extended Buchholz's function), $$\omega_1^{\text{CK}}$$ (Church-Kleene ordinal), $$\omega_\alpha^\text{CK}$$ (admissible ordinal), $$\lambda,\zeta,\Sigma,\gamma$$ (ordinals on infinite time Turing machine), https://googology.wikia.org/wiki/Absolute_infinity?oldid=280565. The letter is known as the Big O in contrast to omicron, which is known as the little O. Omega indicates the end/the last. Isn't it imaginary if it's bigger than itself? It has to be ill-defined like this, or there'd be room for bigger things, and an absolute infinity is supposed to be above any transfinite amount, which CAI does not do properly. However, Sbiis Saibian stated himself that it is "not considered an official transfinite number" and "there is no such thing as a largest number". → The Omega Omnisphere Omegaverse → Absolute Infinitely Infinite of Infinitely Infinite of…of Infinite Perpetually Transcendent Omni-Infinity Omegaverse → The Voidverse → Absolute Infinitely Infinite of Infinitely Infinite of…of Infinite Perpetually Transcendent Omni-Infinity … Even if you try to use a number with a formula to be bigger than BAI by an insane amount, BAI will still be even bigger due to it's property BAI > n. We can prove it if we allow 0=1 to be true. Take your favorite fandoms with you and never miss a beat. Absolute infinity is supposedly the limit of all transfinite ordinals. Even if you try to use a number with a formula to be bigger than BAI by an insane amount, BAI will still be even bigger due to it's property BAI > n. It works a bit like the AD Numberblocksverse, being bigger than verses with sizes supposed to generate sizes bigger than the NBV. We can prove it if we allow n n regardless of the value of n. This causes contradiction, being bigger than itself, so it can also be called the n>n number. Best's Absolute Infinity, aka BAI or Θ, is a number by BestNoobReborn that satisfies the equation BAI > n regardless of the value of n. This causes contradiction, being bigger than itself, so it can also be called the n>n number. If we allow contradictions like this to happen, it's not an imaginary number. This number is a FORBIDDEN NUMBER above and beyond all forbidden numbers. The symbol $\Omega$ was used by Cantor to refer to his idea of the Absolute Infinite. ABSOLUTE INFINITY !!! There is no "absolute answer" as to whether there is an absolute infinity, because whether or not you can have an absolute infinity is a function of what mathematical formalism you use. The concept of Absolute Infinity … To Georg Cantor, who was religious, this number literally represented the totally boundless nature of GOD's power! CAI's only defined as the set of every ordinal. Double exponentiated polynomial omega level, Triple exponentiated polynomial omega level, https://googologytesting.fandom.com/wiki/Best%27s_Absolute_Infinity?oldid=26385.