diff --git a/Concurrent Systems/notes/5 - Software Transactional Memory.md b/Concurrent Systems/notes/5 - Software Transactional Memory.md
index ccf2149..8eb9eac 100644
--- a/Concurrent Systems/notes/5 - Software Transactional Memory.md	
+++ b/Concurrent Systems/notes/5 - Software Transactional Memory.md	
@@ -120,14 +120,14 @@ So for X, I don't just have to track "who modified X", but also "who modified "Y
 
 We have n processes; process $p_i$ has
 - for every X, a local copy `lc(XX)` of the implementation of X
-- $p\_depend_i[1…m]$ s.t. $p\_depend_i[X]$ is the sequence number of the last val of X (directly or indirectly) known by $p_i$
+- $p\_depend_i[1…m]$ s.t. $p\_depend_i[X]$ is the sequence number of the last value of X (directly or indirectly) known by $p_i$
 
 Every transaction T issues by $p_i$ has:
 - `read_set(T)` and `write_set(T)`
 - $t\_depend_{T}[1…m]$ a local copy of $p\_depend_i$ (this is used in the optimistic execution, not to change $p\_depend_{i}$ if T aborts)
 
 ```
-begin_T() :=
+begin_T(i) :=
 	read_set(T), write_set(T) <- ∅
 	t_depend_T <- p_depend_i