Recorded work from Wednesday.

monoid-design.md

@@ -144,16 +144,16 @@ Problem: Given a list of numbers, compute their total.
 ## Monoid Identification
 
 *   Interpretation of input elements as actions:
-    *   …
+    *   An element `a` in the input is an instruction to "add `a` to the total".
 *   Combination of two actions:
-    *   …
+    *   If we add `a` and then add `b`, altogether we add `a + b`.
 *   Representation of actions:
-    *   …
+    *   We can represent any action by storing how much to add to the total.
 *   Identity element:
-    *   …
+    *   Solving `e + x = x + e = x` gives us `e = 0`.
 
 *   Monoid:
-    *   `A = (…, …, …)`
+    *   `A = (𝐑, +, 0)`
 
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@@ -164,16 +164,16 @@ Problem: Given a list of numbers, compute their product.
 ## Monoid Identification
 
 *   Interpretation of input elements as actions:
-    *   …
+    *   An element `a` in the input is an instruction to "multiply by `a`".
 *   Combination of two actions:
-    *   …
+    *   If we multiply by `a` and then we multiply by `b`, altogether we multiply by `a*b`.
 *   Representation of actions:
-    *   …
+    *   We can represent any action by storing the number to multiply by.
 *   Identity element:
-    *   …
+    *   Solving `e * x = x * e = x` gives us `e = 1`.
 
 *   Monoid:
-    *   `P = (…, …, …)`
+    *   `P = (𝐑, *, 1)`
 
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