User:Augigogigi/SbOCF: Difference between revisions
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sbocf is bla bla bla limit is bla bla bla |
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== Definition == |
== Definition == |
Latest revision as of 20:19, 30 August 2023
sbocf
Definition[edit | edit source]
- \( T_{a}(b) = \)
- \( \tau(a) = \)
- \( \kappa(0) = \)
Fundamental Sequences[edit | edit source]
bla bla bla function:
\begin{align} [] : \text{S} \times \mathbb{N} \rightarrow& \text{S} \\ (\text{S},n) \mapsto& \text{S}[n] \end{align}
bla bla bla bla bla
Analysis[edit | edit source]
Expression | Shorthand |
---|---|
\( \tau(a) \) | \( \Omega_{a} \) |
\( \tau(B+a) \) | \( M_{a} \) |
\( \tau(B\cdot2+a) \) | \( N_{a} \) |
\( \tau(B^{2}+a) \) | \( G_{a} \) |
SbOCF | Ordinal | Xi | BMS |
---|---|---|---|
\( T_{\tau(0)}(0) \) | \( 1 \) | - | \( (0) \) |
\( T_{\tau(0)}(1) \) | \( \omega \) | - | \( (0)(1) \) |
\( T_{\tau(0)}(2) \) | \( \omega^{2} \) | - | \( (0)(1)(1) \) |
\( T_{\tau(0)}(T_{\tau(0)}(0)) \) | \( \omega^{\omega} \) | - | \( (0)(1)(2) \) |
\( T_{\tau(0)}(T_{\tau(0)}(T_{\tau(0)}(0))) \) | \( \omega^{\omega^{\omega}} \) | - | \( (0)(1)(2)(3) \) |
\( T_{\tau(0)}(\tau(0)) \) | \( \varepsilon_{0} \) | - | \( (0,0)(1,1) \) |
\( T_{\tau(0)}(\tau(0)+1) \) | \( \varepsilon_{0}\cdot\omega \) | - | \( (0,0)(1,1)(1,0) \) |
\( T_{\tau(0)}(\tau(0)+T_{\tau(0)}(0)) \) | \( \varepsilon_{0}\cdot\omega^{\omega} \) | - | \( (0,0)(1,1)(1,0)(2,0) \) |
\( T_{\tau(0)}(\tau(0)+\tau(0)) \) | \( \varepsilon_{0}^{2} \) | - | \( (0,0)(1,1)(1,0)(2,1) \) |
\( T_{\tau(0)}(\tau(0)\cdot\omega) \) | \( \varepsilon_{0}^{\omega} \) | - | \( (0,0)(1,1)(1,1) \) |