typos

Author: rzach

content/methods/induction/inductive-definitions.tex

@@ -15,7 +15,7 @@
 be defined which explain how to get new objects of that kind from old
 objects of that kind.  For instance, we often define special kinds of
 sequences of symbols, such as the terms and !!{formula}s of a
-language, by induction.  For a simple example, consider strings of
+language, by induction.  For a simple example, consider strings
 consisting of letters $\mathrm{a}$, $\mathrm{b}$, $\mathrm{c}$,
 $\mathrm{d}$, the symbol~$\circ$, and brackets $[$ and $]$, such as
 ``$[[\mathrm{c} \circ \mathrm{d}][$'', ``$[\mathrm{a}[]\circ]$'',

content/methods/proofs/inference-patterns.tex

@@ -232,8 +232,8 @@ \subsection{Proving an Existence Claim}
 When asked to prove an existence claim, the question will usually be
 of the form ``prove that there is an~$x$ such that $\dots x \dots$'',
 i.e., that some object that has the property described by ``$\dots x
-\dots$''. In this case you'll have to identify a suitable object show
-that is has the required property.  This sounds straightforward, but a
+\dots$''. In this case you'll have to identify a suitable object and show
+that it has the required property.  This sounds straightforward, but a
 proof of this kind can be tricky. Typically it involves
 \emph{constructing} or \emph{defining} an object and proving that the
 object so defined has the required property. Finding the right object