diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md
index 14a7eb7..3cb76c8 100644
--- a/Concurrent Systems/notes/6 - Atomicity.md	
+++ b/Concurrent Systems/notes/6 - Atomicity.md	
@@ -30,4 +30,8 @@ $\hat{H}$ is linearizable if $\hat{H}|_{X}$ is linearizable, for all X in H
 (it is good to linearize complex traces)
 
 For all X, let $\hat{S}_{X}$ be a linearization of $\hat{H}_{X}$
-	- $\hat{S}_{X} def$
\ No newline at end of file
+	- $\hat{S}_{X}$ defines a total order on the operations on X (call it $\to_{X}$)
+
+Let $\to$ denote $\to_{H} \cup \bigcup_{X \in H} \to _{X}$
+
+...
\ No newline at end of file