book: Fix typo

book/src/design/proving-system/comparison.md

@@ -47,7 +47,7 @@ Halo 2's polynomial commitment scheme differs from Appendix A.2 of BCMS20 in two
      sampling $z$.
 
 2. The $\text{PC}_\text{DL}.\text{SuccinctCheck}$ subroutine (Figure 2 of BCMS20) computes
-   the initial group element $C_0$ by adding $[v] H' = [v \epsilon] H$, which requires two
+   the initial group element $C_0$ by adding $[v] H' = [v \xi_0] H$, which requires two
    scalar multiplications. Instead, we subtract $[v] G_0$ from the original commitment $P$,
    so that we're effectively opening the polynomial at the point to the value zero. The
    computation $[v] G_0$ is more efficient in the context of recursion because $G_0$ is a

book/src/design/proving-system/lookup.md

@@ -1,6 +1,6 @@
 # Lookup argument
 
-halo2 uses the following lookup technique, which allows for lookups in arbitrary sets, and
+Halo2 uses the following lookup technique, which allows for lookups in arbitrary sets, and
 is arguably simpler than Plookup.
 
 ## Note on Language
@@ -147,7 +147,7 @@ soundness is not affected.
 
 ## Generalizations
 
-halo2's lookup argument implementation generalizes the above technique in the following
+Halo2's lookup argument implementation generalizes the above technique in the following
 ways:
 
 - $A$ and $S$ can be extended to multiple columns, combined using a random challenge. $A'$