Address reviews

- fix typo

- replace `/=` with `≠` in comments

book/src/design/gadgets/decomposition.md

@@ -105,7 +105,7 @@ We now explain how all of these constraints are Plonk encoded:
 
 1) We don't enforce this check in the $K$-high-low decomp gadget, but it's easily represented as the degree-1 constraint $\alpha - (2^K h + \ell) = 0$ when $\alpha$ is in the base field (i.e. when $m = b$). When $\alpha$ is not in the base field, this constraint can't be encoded without transporting $h$ and $\ell$ to $\alpha$'s field.
 
-2) The condition $\ell < 2^K$ is encoded using the [power-of-2 range check gadget](#pow2-rc)to compute a value that is zero when $\ell < 2^K$. Behind the scenes this involves two table lookups and a small degree constraint; see the power-of-2 range check docs for more details.
+2) The condition $\ell < 2^K$ is encoded using the [power-of-2 range check gadget](#pow2-rc) to compute a value that is zero when $\ell < 2^K$. Behind the scenes this involves two table lookups and a small degree constraint; see the power-of-2 range check docs for more details.
 
 3) The condition $h \le H$ is encoded using the [generic range check gadget](#generic-rc) to compute a value that is zero when $h \le H$. Behind the scenes this involves various small degree constraints and lookups; see the generic range check docs for more details.
 

halo2_gadgets/src/utilities/high_low_decomp.rs

@@ -172,7 +172,7 @@ where
             // Constrain `h = h_max`, where `h_max = H`, the high
             // `N-K` bits of the field modulus.
             let h_is_max = h.clone() - h_max;
-            // Constrain `h /= h_max` for use in constraining
+            // Constrain `h ≠ h_max` for use in constraining
             // `(h = h_max) => (l = 0)`.
             //
             // This one is a little subtle: constraints are
@@ -208,7 +208,7 @@ where
             //    satisfied. I.e. if c is satisfied then d is
             //    satisfied, i.e. (c => d) when c is true.
             //
-            // 2) if c /= 0, then (c => d) is true independent of
+            // 2) if c ≠ 0, then (c => d) is true independent of
             //    d. Now either ((1 - c*eta) * d) is zero (true),
             //    because eta was chosen correctly, or ((1 -
             //    c*eta) * d) is non-zero (false), and the
@@ -230,7 +230,7 @@ where
             //   - already checked in the assignment function using strict range check
             // - h = h_max => l = 0
             //   - which is equivalent to
-            //     - h /= h_max \/ l = 0
+            //     - h ≠ h_max \/ l = 0
             // - h <= h_max
             //   - already checked in the assignment function using strict range check
             Constraints::with_selector(

halo2_gadgets/src/utilities/pow2_range_check.rs

@@ -191,7 +191,7 @@ impl<F: PrimeFieldBits, const K: usize> Config<F, K> {
         // If `r == 0`, we just assign `low_r_bits` to zero. We use
         // `assign_advice_from_constant`, so this guarantees that `r =
         // 0` / the prover can't cheat, and we don't need to do the
-        // `short_range_check` from the `r /= 0` branch.
+        // `short_range_check` from the `r ≠ 0` branch.
         let low_r_bits = if r == 0 {
             layouter.assign_region(
                 || "low_r_bits (== 0)",