vault backup: 2026-03-09 17:46:37

DAS/Functions.md

@@ -18,7 +18,6 @@ For any $x in X$ the output $f(x)$ is an element of $Y$.
 ### Injectivity
 A function is _injective_ if every element in $y in f(x)$ has _at most_ one matching $x in X$.
 - $forall y in Y,exists excl x in X : f(x) = y$
-
 ### Surjectivity
 A function is _surjective_ if every element $y in Y$ has _at minimum_ one matching $x in X$
 - $forall y in Y, exists x in X : f(x) = y$

DAS/Relations.md

@@ -50,12 +50,21 @@ $$
 "Compute" Q^top compose R "with:"\
 Q = {(2, 2), (3, 3), (2, 1)} \
 R = {(1, 2), (3, 3), (3, 1)} \
-\
-"1. Apply converse to Q:"\
-Q^top = {(2, 2), (3, 3), (1, 2)}
-
-"2. Check "
 $$
+### 1. Apply converse to $Q$:
+$$
+Q^top = {(2, 2), (3, 3), (1, 2)}
+$$
+### 2. Perform Composition:
+Look at each pair in $R$, check if $Q^top$ has a pair starting with se second element in that pair:
+
+$$
+(1, 2) -> (2, 2) => (1, 2) \
+(3, 3) -> (3, 3) => (3, 3) \
+(3, 1) -> (1, 2) => (3, 2)
+$$
+### 3. Result:
+$$ Q^top compose R = {(1, 2), (3, 2), (3, 3)} $$
 
 ## Orders
 An **Order** is a mathematical way to sort, rank or compare elements within a set, where some elements come "before" and "after" others.