small changes

This commit is contained in:
Josia Pietsch 2024-01-10 22:22:28 +01:00
parent 73b8fb0dd1
commit 8ce92917ed
Signed by: josia
GPG key ID: E70B571D66986A2D
4 changed files with 3 additions and 3 deletions

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@ -9,7 +9,7 @@
\begin{enumerate}[(a)] \begin{enumerate}[(a)]
\item $0$ is an ordinal, and if $\alpha$ is \item $0$ is an ordinal, and if $\alpha$ is
an ordinal, so is $\alpha + 1$. an ordinal, so is $\alpha + 1$.
\item If $\alpha$ is an ordinal and $x \in a$, \item If $\alpha$ is an ordinal and $x \in \alpha$,
then $x$ is an ordinal. then $x$ is an ordinal.
\item If $\alpha, \beta$ are ordinals \item If $\alpha, \beta$ are ordinals
and $\alpha \subseteq \beta$, and $\alpha \subseteq \beta$,

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@ -54,7 +54,7 @@ An alternative way of formulating this is
Let $D$ be a class of triples Let $D$ be a class of triples
such that for all $u,x$ there is exactly such that for all $u,x$ there is exactly
one $y$ with $(u,x,y) \in D$ one $y$ with $(u,x,y) \in D$
(basicalls $(u,x) \mapsto y$ is a function). (basically $(u,x) \mapsto y$ is a function).
Then there is a unique function $f$ on $A$ Then there is a unique function $f$ on $A$
such that for all $x \in A$, such that for all $x \in A$,

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@ -158,7 +158,7 @@ This $F$ is called the \vocab{rank function} for $(A, R)$.
\] \]
and and
\[ \[
\rk_R \rank(R) \coloneqq \ran(F). \rank(R) \coloneqq \ran(F).
\] \]
In the special case that $R$ is a linear order on $A$, In the special case that $R$ is a linear order on $A$,