diff --git a/content/blog/01_spa_agda_lattices.md b/content/blog/01_spa_agda_lattices.md
index 655ee83..a87afa4 100644
--- a/content/blog/01_spa_agda_lattices.md
+++ b/content/blog/01_spa_agda_lattices.md
@@ -263,8 +263,21 @@ ours, the analog to `min` is "greatest lower bound", or "the largest value
 that's smaller than both inputs". Such a function is denoted as \\(a\\sqcap b\\).
 As for what it means, where \\(s_1 \\sqcup s_2\\) means "combine two signs where
 you don't know which one will be used" (like in an `if`/`else`), 
-\\(s_1 \\sqcap s_2\\) means "combine two signs where you know both of
-them to be true". For example, \\((+\ \\sqcap\ ?)\ =\ +\\), because a variable
+\\(s_1 \\sqcap s_2\\) means "combine two signs where you know
+{{< sidenote "right" "or-join-note" "both of them to be true" -7 >}}
+If you're familiar with <a href="https://en.wikipedia.org/wiki/Boolean_algebra">
+Boolean algebra</a>, this might look a little bit familiar to you. In fact,
+the symbol for "and" on booleans is \(\land\). Similarly, the symbol
+for "or" is \(\lor\). So, \(s_1 \sqcup s_2\) means "the sign is \(s_1\) or \(s_2\)",
+or "(the sign is \(s_1\)) \(\lor\) (the sign is \(s_2\))". Similarly,
+\(s_1 \sqcap s_2\) means "(the sign is \(s_1\)) \(\land\) (the sign is \(s_2\))".
+Don't these symbols look similar?<br>
+<br>
+In fact, booleans with \((\lor)\) and \((\land)\) satisfy the semilattice
+laws we've been discussing, and together form a lattice (to which I'm building
+to in the main body of the text). The same is true for the set union and
+intersection operations, \((\cup)\) and \((\cap)\).
+{{< /sidenote >}}". For example, \\((+\ \\sqcap\ ?)\ =\ +\\), because a variable
 that's both "any sign" and "positive" must be positive.
 
 There's just one hiccup: what's the greatest lower bound of `+` and `-`?