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Mockingbird edits

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Mark 2023-03-30 20:55:05 -07:00
parent 48ac646ee4
commit 1761619d66
3 changed files with 9 additions and 7 deletions
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2
Advanced/Mock a Mockingbird/parts/00 intro.tex
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@ -8,7 +8,7 @@ Bird $AB$ is, by definition, $A$'s response to $B$.
As you wander around this forest, you quickly discover two interesting facts: As you wander around this forest, you quickly discover two interesting facts:
\begin{enumerate}[itemsep = 1mm] \begin{enumerate}[itemsep = 1mm]
\item $A$'s responds to $B$ mustn't be the same as $B$'s response to $A$. \item $A$'s response to $B$ mustn't be the same as $B$'s response to $A$.
\item Given three birds $A$, $B$, and $C$, $(AB)C$ and $A(BC)$ are not necessarily the same bird. \\ \item Given three birds $A$, $B$, and $C$, $(AB)C$ and $A(BC)$ are not necessarily the same bird. \\
Bird $A(BC)$ is $A$'s response to bird $BC$, while $(AB)C$ is $AB$'s response to $C$. \\ Bird $A(BC)$ is $A$'s response to bird $BC$, while $(AB)C$ is $AB$'s response to $C$. \\
Thus, $ABC$ is ambiguous. Parenthesis are mandatory. Thus, $ABC$ is ambiguous. Parenthesis are mandatory.

10
Advanced/Mock a Mockingbird/parts/01 tmam.tex
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@ -29,7 +29,7 @@ Complete his proof.
\vfill \vfill
\problem{} \problem{}
We say a bird $A$ is \textit{egocentric} if it is fond if itself. \\ We say a bird $A$ is \textit{egocentric} if it is fond of itself. \\
Show that the laws of the forest guarantee that at least one bird is egocentric. Show that the laws of the forest guarantee that at least one bird is egocentric.
@ -56,7 +56,7 @@ Show that the laws of the forest guarantee that at least one bird is egocentric.
\definition{} \definition{}
We say a bird $A$ is \textit{agreeable} if for all birds $B$, there is at least one bird $x$ on which $A$ and $B$ agree. \\ We say a bird $A$ is \textit{agreeable} if for all birds $B$, there is at least one bird $x$ on which $A$ and $B$ agree. \\
In other words, $A$ is agreeable if $Ax = Bx$ for some $x$ for all $B$. In other words, $A$ is agreeable if given any $B$, we can find a bird $x$ satisfying $Ax = Bx$.
\problem{} \problem{}
Is the Mockingbird agreeable? Is the Mockingbird agreeable?
@ -71,7 +71,7 @@ Is the Mockingbird agreeable?
\problem{} \problem{}
Take two birds $A$ and $B$. Let $C$ be their composition. \\ Take two birds $A$ and $B$. Let $C$ be their composition. \\
Show that $A$ must be agreeable if $C$ is agreeable. Show that if $C$ is agreeable, $A$ is agreeable.
\begin{alltt} \begin{alltt}
\cmnt{Given information} \cmnt{Given information}
let A, B let A, B
@ -125,9 +125,11 @@ Given three arbitrary birds $A$, $B$, and $C$, show that there exists a bird $D$
\vfill \vfill
\problem{} \definition{}
We say two birds $A$ and $B$ are \textit{compatible} if there are birds $x$ and $y$ so that $Ax = y$ and $By = x$. \\ We say two birds $A$ and $B$ are \textit{compatible} if there are birds $x$ and $y$ so that $Ax = y$ and $By = x$. \\
Note that $x$ and $y$ may be the same bird. \\ Note that $x$ and $y$ may be the same bird. \\
\problem{}
Show that any two birds in this forest are compatible. \\ Show that any two birds in this forest are compatible. \\
\begin{alltt} \begin{alltt}
let A, B let A, B

4
Advanced/Mock a Mockingbird/parts/02 kestrel.tex
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@ -28,12 +28,12 @@ Say $A$ is fixated on $B$. Is $A$ fond of $B$?
\definition{} \definition{}
The \textit{Kestrel} $K$ is defined by the following relationship: The \textit{Kestrel} $K$ is defined by the following relationship:
$$ $$
(Kx)y = x (Kx)y = x~~~\forall x, y
$$ $$
In other words, this means that for every bird $x$, the bird $Kx$ is fixated on $x$. In other words, this means that for every bird $x$, the bird $Kx$ is fixated on $x$.
\problem{} \problem{}
Show that an egocenteric Kestrel is hopelessly egocentric Show that an egocenteric Kestrel is hopelessly egocentric.
\begin{solution} \begin{solution}
\begin{alltt} \begin{alltt}