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Mark 2023-04-03 11:09:02 -07:00
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Advanced/Mock a Mockingbird/parts/02 kestrel.tex
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@ -1,7 +1,7 @@
\section{The Curious Kestrel} \section{The Curious Kestrel}
\definition{} \definition{}
Recall that a bird is \textit{egocenteric} if it is fond of itself. \\ Recall that a bird is \textit{egocentric} if it is fond of itself. \\
A bird is \textit{hopelessly egocentric} if $Bx = B$ for all birds $x$. A bird is \textit{hopelessly egocentric} if $Bx = B$ for all birds $x$.
\definition{} \definition{}
@ -33,7 +33,7 @@ $$
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 egocentric Kestrel is hopelessly egocentric.
\begin{solution} \begin{solution}
\begin{alltt} \begin{alltt}
@ -58,7 +58,7 @@ Given the Law of Composition and the Law of the Mockingbird, show that at least
\end{helpbox} \end{helpbox}
\begin{solution} \begin{solution}
The final piece is a lemma we proved earler: \\ The final piece is a lemma we proved earlier: \\
Any bird is fond of at least one bird Any bird is fond of at least one bird
\begin{alltt} \begin{alltt}
@ -115,7 +115,7 @@ Show that if $K$ is fond of $Kx$, $K$ is fond of $x$.
An egocentric Kestrel must be extremely lonely. Why is this? An egocentric Kestrel must be extremely lonely. Why is this?
\begin{solution} \begin{solution}
If a Kestrel is egocenteric, it must be the only bird in the forest! If a Kestrel is egocentric, it must be the only bird in the forest!
\begin{alltt} \begin{alltt}
\lineno{} \cmnt{Given} \lineno{} \cmnt{Given}