From 1761619d6627634052d4c3db601e0da5c91240bd Mon Sep 17 00:00:00 2001 From: Mark Date: Thu, 30 Mar 2023 20:55:05 -0700 Subject: [PATCH] Mockingbird edits --- Advanced/Mock a Mockingbird/parts/00 intro.tex | 2 +- Advanced/Mock a Mockingbird/parts/01 tmam.tex | 10 ++++++---- Advanced/Mock a Mockingbird/parts/02 kestrel.tex | 4 ++-- 3 files changed, 9 insertions(+), 7 deletions(-) diff --git a/Advanced/Mock a Mockingbird/parts/00 intro.tex b/Advanced/Mock a Mockingbird/parts/00 intro.tex index c0267d7..8e13a24 100644 --- a/Advanced/Mock a Mockingbird/parts/00 intro.tex +++ b/Advanced/Mock a Mockingbird/parts/00 intro.tex @@ -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: \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. \\ 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. diff --git a/Advanced/Mock a Mockingbird/parts/01 tmam.tex b/Advanced/Mock a Mockingbird/parts/01 tmam.tex index 16fee99..55a8af1 100644 --- a/Advanced/Mock a Mockingbird/parts/01 tmam.tex +++ b/Advanced/Mock a Mockingbird/parts/01 tmam.tex @@ -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 diff --git a/Advanced/Mock a Mockingbird/parts/02 kestrel.tex b/Advanced/Mock a Mockingbird/parts/02 kestrel.tex index b28b349..0e4f900 100644 --- a/Advanced/Mock a Mockingbird/parts/02 kestrel.tex +++ b/Advanced/Mock a Mockingbird/parts/02 kestrel.tex @@ -28,12 +28,12 @@ Say $A$ is fixated on $B$. Is $A$ fond of $B$? \definition{} 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 $x$. \problem{} -Show that an egocenteric Kestrel is hopelessly egocentric +Show that an egocenteric Kestrel is hopelessly egocentric. \begin{solution} \begin{alltt}