auto-update(nvim): 2025-01-06 18:28:44

documents/by-course/math-8/course-notes/dvd.typ

@@ -1,5 +1,5 @@
-#import "@preview/ctheorems:1.1.2": *
-#import "@preview/showybox:2.0.1": showybox
+#import "@preview/ctheorems:1.1.3": *
+#import "@preview/showybox:2.0.3": showybox
 
 #let colors = (
   rgb("#9E9E9E"),
@@ -257,27 +257,33 @@
   shadow: (offset: (x: 2pt, y: 2pt), color: luma(70%)),
 )
 
-#let problem = problem-style("problem", "Problem")
+#let exercise = problem-style("item", "Exercise")
+#let problem = exercise
 
 #let theorem-style = builder-thmbox(
   color: colors.at(6),
   shadow: (offset: (x: 3pt, y: 3pt), color: luma(70%)),
 )
 
-#let theorem = theorem-style("theorem", "Theorem")
-#let lemma = theorem-style("lemma", "Lemma")
-#let corollary = theorem-style("corollary", "Corollary")
+#let example-style = builder-thmbox(
+  color: colors.at(16),
+  shadow: (offset: (x: 3pt, y: 3pt), color: luma(70%)),
+)
+
+#let theorem = theorem-style("item", "Theorem")
+#let lemma = theorem-style("item", "Lemma")
+#let corollary = theorem-style("item", "Corollary")
 
 #let definition-style = builder-thmline(color: colors.at(8))
 
-#let definition = definition-style("definition", "Definition")
-#let proposition = definition-style("proposition", "Proposition")
-#let remark = definition-style("remark", "Remark")
-#let observation = definition-style("observation", "Observation")
+// #let definition = definition-style("definition", "Definition")
+#let proposition = definition-style("item", "Proposition")
+#let remark = definition-style("item", "Remark")
+#let observation = definition-style("item", "Observation")
 
-#let example-style = builder-thmline(color: colors.at(16))
+// #let example-style = builder-thmline(color: colors.at(16))
 
-#let example = example-style("example", "Example").with(numbering: none)
+#let example = example-style("item", "Example").with(numbering: none)
 
 #let proof(body, name: none) = {
   thmtitle[Proof]
@@ -289,3 +295,26 @@
   h(1fr)
   $square$
 }
+
+#let fact = thmplain(
+  "item",
+  "Fact",
+  titlefmt: strong,
+  separator: ".",
+
+  inset: 0pt,
+)
+#let abuse = thmplain(
+  "item",
+  "Abuse of Notation",
+  titlefmt: strong,
+  separator: ".",
+  inset: 0pt,
+)
+#let definition = thmplain(
+  "item",
+  "Definition",
+  titlefmt: strong,
+  separator: ".",
+  inset: 0pt,
+)

documents/by-course/math-8/course-notes/main.typ

@@ -62,7 +62,8 @@ Definitions barely worth considering. Included purely for posterity.
   $x^2 + 6x + 8 = 0$
 ]
 
-Propositions may be stated in the formalism of mathematics using connectives, as *propositional forms*.
+Propositions may be stated in the formalism of mathematics using connectives,
+as *propositional forms*.
 
 #definition("Propositional forms")[
   Let $P$ and $Q$ be propositions. Then:

documents/by-course/pstat-120a/course-notes/main.typ

@@ -21,8 +21,14 @@
 
 == Set theory for dummies
 
-A terse introduction to elementary set theory and the basic operations upon
-them.
+A terse introduction to elementary naive set theory and the basic operations
+upon them.
+
+#remark[
+  Keep in mind that without $cal(Z F C)$ or another model of set theory that
+  resolves fundamental issues, our set theory is subject to paradoxes like
+  Russell's.
+]
 
 #definition[
   A Set is a collection of elements.
@@ -51,7 +57,7 @@ With arbitrary sets $A$, $B$:
 + $a in.not A$ ($a$ is not a member of the set $A$)
 + $A subset.eq B$ (Set theory: $A$ is a subset of $B$) (Stats: $A$ is a sample space in $B$)
 + $A subset B$ (Proper subset: $A != B$)
-+ $A^c$ or $A'$ (read "complement of $A$")
++ $A^c$ or $A'$ (read "complement of $A$", and gives all the elements in the universal set not in $A$)
 + $A union B$ (Union of $A$ and $B$. Gives a set with both the elements of $A$ and $B$)
 + $A sect B$ (Intersection of $A$ and $B$. Gives a set consisting of the elements in *both* $A$ and $B$)
 + $A \\ B$ (Set difference. The set of all elements of $A$ that are not also in $B$)
@@ -64,12 +70,19 @@ We can also write a few of these operations precisely as set comprehensions.
 + $A sect B = {x | x in A and x in B}$ (here $and$ is the logical AND)
 + $A \\ B = {a | a in A and a in.not B}$
 + $A times B = {(a,b) | forall a in A, forall b in B}$
++ $A' = A sect Omega$, where $Omega$ is the _universal set_.
+
+#definition[
+  The universal set $Omega$ is the set of all objects in a given set
+  theoretical universe.
+]
 
 Take a moment and convince yourself that these definitions are equivalent to
 the previous ones.
 
 #example[The real plane][
-  The real plane $RR^2$ can be defined as a Cartesian product of $RR$ with itself.
+  The real plane $RR^2$ can be defined as a Cartesian product of $RR$ with
+  itself.
 
   $ RR^2 = RR times RR $
 ]
@@ -118,10 +131,7 @@ When a set is uncountably infinite, its cardinality is greater than $aleph_0$.
   + The real numbers in the interval $[0,1]$.
 ]
 
-#remark[Bijection][
+#fact[
   If a set is countably infinite, then it has a bijection with $ZZ$. This means
   every set with cardinality $aleph_0$ has a bijection to $ZZ$.
 ]
-
-
-