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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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Advanced/Mock a Mockingbird/parts/01 tmam.tex
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@ -29,7 +29,7 @@ Complete his proof.
\vfill
\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.
@ -56,7 +56,7 @@ Show that the laws of the forest guarantee that at least one bird is egocentric.
\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. \\
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{}
Is the Mockingbird agreeable?
@ -71,7 +71,7 @@ Is the Mockingbird agreeable?
\problem{}
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}
\cmnt{Given information}
let A, B
@ -125,9 +125,11 @@ Given three arbitrary birds $A$, $B$, and $C$, show that there exists a bird $D$
\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 $By = x$. \\
Note that $x$ and $y$ may be the same bird. \\
\problem{}
Show that any two birds in this forest are compatible. \\
\begin{alltt}
let A, B