Reorganizing C declarations file.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -254,7 +254,7 @@
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-    "combinatorics/permutations.md": "efd0820ab3cc7faa5b2df3fe40105110",
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@@ -269,7 +269,7 @@
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     "c17/index.md": "78576ee41d0185df82c59999142f4edb",
     "c17/escape-sequences.md": "a8b99070336878b4e8c11e9e4525a500",
-    "c17/declarations.md": "ab6d44e48b0c1c8d98cd409721cc2c53",
+    "c17/declarations.md": "eb289ab10ccb8b1a7981ceedbbdda2ad",
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-    "algebra/set.md": "b4d5ce4b914abe5063bf6043cf7a0aee",
+    "algebra/set.md": "30a13f1db3c53dbff179eca2873d7732",
     "algebra/boolean.md": "fc47edb7d0080b73ce1ce0d3e0e16d7d",
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@@ -520,7 +520,7 @@
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     "_journal/2024-06/2024-06-05.md": "b06a0fa567bd81e3b593f7e1838f9de1",
-    "set/relations.md": "84a66a74805014d3b88ea5e8a3e763bc",
+    "set/relations.md": "9f59faf0f21dfe49ad89ac6e8115d269",
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     "ontology/rdf/index.md": "36424c9bad6088cdee67f74e3b8a019f",
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     "ontology/philosophy/nominalism.md": "46245c644238157e15c7cb6def27d90a",
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+    "_journal/2024-08-04.md": "f3675ba4cd33f16a5695732bbe10473e",
+    "_journal/2024-08/2024-08-03.md": "7c1d3dbaf47d1120bb879110e827d1b3",
+    "c17/pointers.md": "c80957f5cab7403b85bcabcc9ce983ef"
   },
   "fields_dict": {
     "Basic": [

notes/_journal/2024-08-04.md

@@ -0,0 +1,9 @@
+---
+title: "2024-08-04"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)

notes/_journal/2024-08/2024-08-03.md

@@ -8,4 +8,5 @@ title: "2024-08-03"
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 
-* Additional notes on binary search trees.
+* Additional notes on binary search trees.
+* Notes on (strong) [[relations#Connected|connectivity]] of relations.

notes/algebra/set.md

@@ -207,7 +207,7 @@ END%%
 %%ANKI
 Basic
 Assume AoC and $H(j) \neq \varnothing$ for all $j \in I$. What does $\bigtimes_{i \in I} H(i)$ evaluate to?
-Back: A non-empty set.
+Back: $\{f \mid f \text{ is a function with domain } I \text{ and } \forall i \in I, f(i) \in H(i)\}$
 Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 <!--ID: 1720964209709-->
 END%%

notes/c17/declarations.md

@@ -8,6 +8,323 @@ tags:
 
 ## Overview
 
+C declarations were designed so that the declaration of an object looks like the use of the object. This isn't quite true - keywords like `volatile` and `const` only exist in declarations - but for the most part, this philosophy can be leveraged to read C declarations.
+
+## Declarators
+
+A **declarator** in C is roughly an identifier along with pointers, function brackets, or array indications. Pointers will look like one of:
+
+* `*`
+* `* const`
+* `* volatile`
+* `* const volatile`
+* `* volatile const`
+
+whereas **direct declarators** will look like one of:
+
+* `identifier`
+* `identifier[size]`
+* `identifier(args)`
+* `(declarator)`
+
+%%ANKI
+Basic
+What two qualifiers can be found on a pointer?
+Back: `const` and `volatile`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892098-->
+END%%
+
+## Declarations
+
+A **declaration** consists of at least one type-specifier (e.g. `signed short`), storage class (e.g. `static`), and/or type qualifier (e.g. `const`) as well as one or more declarators.
+
+%%ANKI
+Basic
+How many declarators does a declaration have?
+Back: At least one.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892100-->
+END%%
+
+%%ANKI
+Basic
+How many declarations does a declarator have?
+Back: N/A.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892101-->
+END%%
+
+%%ANKI
+Basic
+Which part of the following are declarators?
+```c
+int* a, b;
+```
+Back: `* a` and `b`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892102-->
+END%%
+
+%%ANKI
+Basic
+Which part of the following are declarations?
+```c
+int* a, b;
+```
+Back: The entire line is a single declaration.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892103-->
+END%%
+
+%%ANKI
+Basic
+Which part of the following declaration is the declarator?
+```c
+const int *const x;
+```
+Back: `*const x`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892104-->
+END%%
+
+%%ANKI
+Basic
+Which part of the following declaration is the type specifier?
+```c
+const int *const x;
+```
+Back: `int`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892105-->
+END%%
+
+%%ANKI
+Basic
+Which part of the following declaration is the type qualifier?
+```c
+const int *const x;
+```
+Back: The first `const`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892106-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `x` in the following?
+```c
+const int *const x, y;
+```
+Back: `const int* const`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892107-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `y` in the following?
+```c
+const int *const x, y;
+```
+Back: `const int`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892108-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `x` in the following?
+```c
+#define int_ptr int *
+int_ptr x, y;
+```
+Back: `int *`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892109-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `y` in the following?
+```c
+#define int_ptr int *
+int_ptr x, y;
+```
+Back: `int`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892110-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `x` in the following?
+```c
+typedef int_ptr int *
+int_ptr x, y;
+```
+Back: `int *`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892111-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `y` in the following?
+```c
+typedef int_ptr int *
+int_ptr x, y;
+```
+Back: `int *`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892112-->
+END%%
+
+Declarations can be read by complying with the precedence rules outlined below:
+
+1. Find the name of the declaration.
+2. Obey the following precedence rules:
+	1. Parentheses grouping together parts of a declaration
+	2. Postfix operators `()` and `[]`
+	3. Prefix operator: the asterisk `*` denoting "pointer to"
+3. If `const` and/or `volatile` keyword is next to a type specifier, it applies to the type specifier. Otherwise it applies to the pointer asterisk on its immediate left.
+
+%%ANKI
+Basic
+In the precedence rules for C declarations, what available postfix operators are there?
+Back: `()` and `[]`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892113-->
+END%%
+
+%%ANKI
+Basic
+In the precedence rules for C declarations, what available prefix operators are there?
+Back: Just `*`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892114-->
+END%%
+
+%%ANKI
+Basic
+In the precedence rules for C declarations, what available type qualifiers are there?
+Back: `const` and `volatile`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892115-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+char *const *(*foo)();
+```
+Back: A pointer to a function returning a pointer to a `const` pointer-to-char.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892116-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+char *const *foo();
+```
+Back: A function returning a pointer to a `const` pointer-to-char.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892117-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+int (*(*foo)(void))[3]
+```
+Back: A pointer to a function (accepting `void`)  returning a pointer to an array of `int`s.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892118-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+const int (* volatile foo)[64]
+```
+Back: A `volatile` pointer to an array of `const int`s.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892119-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+const int * const foo;
+```
+Back: A `const` pointer to a `const int`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892120-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+const int * foo;
+```
+Back: A pointer to a `const int`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892121-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+int const * foo;
+```
+Back: A pointer to a `const int`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892122-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+int * const foo;
+```
+Back: A `const` pointer-to-int.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892123-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `foo` in the the following declaration?
+```c
+char *(*foo[10])(int **);
+```
+Back: An array of pointers to functions (accepting `int **`) returning pointer-to-char.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892124-->
+END%%
+
+%%ANKI
+Basic
+What is the type of `signal` in the the following declaration?
+```c
+void (*signal(int sig, void (*func)(int)))(int);
+```
+Back: A function (accepting an `int` and `void (*)(int)`) returning a pointer to a function (accepting an `int`) returning `void`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892125-->
+END%%
+
+### Type Specifiers
+
 Signed      | Unsigned            | 32-bit | 64-bit
 ----------- | ------------------- | ------ | ------
 signed char | unsigned char       | 1      | 1
@@ -210,6 +527,182 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1718281813458-->
 END%%
 
+### Structs
+
+A `struct` is a grouping of data together. It has the following general form:
+
+```c
+struct optional_tag {
+  type_1 ident1;
+  ...
+  type_N identN;
+} optional_var1 ... optional_varM;
+```
+
+%%ANKI
+Basic
+What is the underlined portion of the following declaration called?
+```c
+struct ___ { ... };
+```
+Back: The tag.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892126-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes the `X`'s from one another in the following?
+```c
+struct X { ... } X;
+```
+Back: The first `X` is a tag whereas the second is a variable with type `struct X`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892127-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes the `X`'s from one another in the following?
+```c
+typedef struct X { ... } X;
+```
+Back: The first `X` is a tag whereas the second is an alias for type `struct X`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892128-->
+END%%
+
+### Unions
+
+A `union` is a grouping of data together but with overlaid storage. It has the following general form:
+
+```c
+union optional_tag {
+  type1 ident1;
+  ...
+  typeN identN;
+} optional_var1 ... optional_varN;
+```
+
+%%ANKI
+Basic
+What is the underlined portion of the following declaration called?
+```c
+union ___ { ... };
+```
+Back: The tag.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892129-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes the `X`'s from one another in the following?
+```c
+union X { ... } X;
+```
+Back: The first `X` is a tag whereas the second is a variable with type `union X`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892130-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes the `X`'s from one another in the following?
+```c
+typedef union X { ... } X;
+```
+Back: The first `X` is a tag whereas the second is an alias for type `union X`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892131-->
+END%%
+
+### Enums
+
+An `enum` is a mapping of identifiers with integer values. They have general form:
+
+```c
+enum optional_tag {
+  type1 ident1;
+  ...
+  typeN identN;
+} optional_var1 ... optional_varN;
+```
+
+%%ANKI
+Basic
+What is the underlined portion of the following declaration called?
+```c
+enum ___ { ... };
+```
+Back: The tag.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892132-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes the `X`'s from one another in the following?
+```c
+enum X { ... } X;
+```
+Back: The first `X` is a tag whereas the second is a variable with type `enum X`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892133-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes the `X`'s from one another in the following?
+```c
+typedef enum X { ... } X;
+```
+Back: The first `X` is a tag whereas the second is an alias for type `enum X`.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892134-->
+END%%
+
+%%ANKI
+Basic
+What is the value of `A` in the following?
+```c
+enum X { A, B, C };
+```
+Back: `0`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892135-->
+END%%
+
+%%ANKI
+Basic
+What is the value of `B` in the following?
+```c
+enum X { A, B, C };
+```
+Back: `1`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892136-->
+END%%
+
+%%ANKI
+Basic
+What is the value of `B` in the following?
+```c
+enum X { A=2, B, C };
+```
+Back: `3`
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892137-->
+END%%
+
+%%ANKI
+Basic
+What is the "only advantage" of `enum`s over `#define` according to Linden?
+Back: `enum`s can usually be traced in a debugger.
+Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.
+<!--ID: 1722786892138-->
+END%%
+
 ## Integer Literals
 
 Negative integer literals are typed in a counterintuitive way. When the compiler sees a number of form `-X`, the type of `X` is determined *before* being negated. Promotion rules are as follows:
@@ -415,18 +908,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1714677608769-->
 END%%
 
-## Pointers
-
-Pointers have the same size as the machine's word size since it should be able to refer to any virtual address.
-
-%%ANKI
-Basic
-*Why* does a pointer's size match the machine's word size?
-Back: Because it should be able to refer to any virtual address.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1707493017246-->
-END%%
-
 ## Bibliography
 
 * Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+* Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Programming Languages / C. Mountain View, Cal.: SunSoft Pr, 1994.

notes/c17/pointers.md

@@ -0,0 +1,23 @@
+---
+title: Pointers
+TARGET DECK: Obsidian::STEM
+FILE TAGS: c17
+tags:
+  - c17
+---
+
+## Overview
+
+Pointers have the same size as the machine's word size since it should be able to refer to any virtual address.
+
+%%ANKI
+Basic
+*Why* does a pointer's size match the machine's word size?
+Back: Because it should be able to refer to any virtual address.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1707493017246-->
+END%%
+
+## Bibliography
+
+* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.

notes/combinatorics/permutations.md

@@ -128,12 +128,20 @@ END%%
 
 %%ANKI
 Basic
-*Why* might $0! = 1$ (barring convention)?
+How is the multiplication identity used to justify equality $0! = 1$?
-Back: Because the empty product is $1$, the multiplication identity.
+Back: The empty product is $1$, i.e. the multiplication identity.
 Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
 <!--ID: 1708366788603-->
 END%%
 
+%%ANKI
+Basic
+What combinatorial explanation justifies equality $0! = 1$?
+Back: There is only $1$ way to order $0$ objects.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1722775277862-->
+END%%
+
 %%ANKI
 Basic
 What combinatorial concept explains the number of bijective functions between two finite sets?

notes/ontology/rdf/uri.md

@@ -162,7 +162,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what scheme? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what scheme? $$\text{http://www.example.com/questions/3456/my-document}$$
 Back: `http`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212201466-->
@@ -170,7 +170,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what authority? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what authority? $$\text{http://www.example.com/questions/3456/my-document}$$
 Back: `//www.example.com`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212201450-->
@@ -178,23 +178,23 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what userinfo? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what userinfo? $$\text{http://www.example.com/questions/3456/my-document}$$
-Back: N/A. It is undefined
+Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212472982-->
 END%%
 
 %%ANKI
 Basic
-The following URI has what port? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what port? $$\text{http://www.example.com/questions/3456/my-document}$$
-Back: N/A. It is undefined
+Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212472988-->
 END%%
 
 %%ANKI
 Basic
-The following URI has what host? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what host? $$\text{http://www.example.com/questions/3456/my-document}$$
 Back: `www.example.com`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212472995-->
@@ -202,7 +202,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what path? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what path? $$\text{http://www.example.com/questions/3456/my-document}$$
 Back: `/questions/3456/my-document`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212201416-->
@@ -210,7 +210,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what query? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what query? $$\text{http://www.example.com/questions/3456/my-document}$$
 Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212201460-->
@@ -218,7 +218,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what fragment? $$\text{http://www.example.com/questions/3456/my-document}$$
+The following URI specifies what fragment? $$\text{http://www.example.com/questions/3456/my-document}$$
 Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212201472-->
@@ -228,7 +228,7 @@ END%%
 Cloze
 The authority of a URI has the following generic syntax:
 
-{`[<userinfo>@]`}{`<host>`}{`[:<port>]}
+{`[<userinfo>@]`}{`<host>`}{`[:<port>]`}
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722211744669-->
 END%%
@@ -251,7 +251,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what fragment? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
+The following URI specifies what scheme? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
 Back: `ldap`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212473001-->
@@ -259,7 +259,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what fragment? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
+The following URI specifies what fragment? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
 Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790216-->
@@ -267,7 +267,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what authority? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
+The following URI specifies what authority? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
 Back: `[2001:db8::7]`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790223-->
@@ -275,7 +275,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what query? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
+The following URI specifies what query? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
 Back: `objectClass?one`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790228-->
@@ -283,7 +283,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what path? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
+The following URI specifies what path? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
 Back: `/c=GB`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790232-->
@@ -291,7 +291,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what scheme? $$\text{tel:+1-816-555-1212}$$
+The following URI specifies what scheme? $$\text{tel:+1-816-555-1212}$$
 Back: `tel`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790236-->
@@ -299,7 +299,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what authority? $$\text{tel:+1-816-555-1212}$$
+The following URI specifies what authority? $$\text{tel:+1-816-555-1212}$$
 Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790241-->
@@ -307,7 +307,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what path? $$\text{tel:+1-816-555-1212}$$
+The following URI specifies what path? $$\text{tel:+1-816-555-1212}$$
 Back: `+1-816-555-1212`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790247-->
@@ -315,7 +315,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what query? $$\text{tel:+1-816-555-1212}$$
+The following URI specifies what query? $$\text{tel:+1-816-555-1212}$$
 Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790252-->
@@ -323,7 +323,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what fragment? $$\text{tel:+1-816-555-1212}$$
+The following URI specifies what fragment? $$\text{tel:+1-816-555-1212}$$
 Back: N/A. It is undefined.
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790258-->
@@ -331,7 +331,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what scheme? $$\text{telnet://192.0.2.16:80/}$$
+The following URI specifies what scheme? $$\text{telnet://192.0.2.16:80/}$$
 Back: `telnet`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790265-->
@@ -339,7 +339,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what authority? $$\text{telnet://192.0.2.16:80/}$$
+The following URI specifies what authority? $$\text{telnet://192.0.2.16:80/}$$
 Back: `192.0.2.16:80`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790272-->
@@ -347,7 +347,7 @@ END%%
 
 %%ANKI
 Basic
-The following URI has what path? $$\text{telnet://192.0.2.16:80/}$$
+The following URI specifies what path? $$\text{telnet://192.0.2.16:80/}$$
 Back: `/`
 Reference: “Uniform Resource Identifier.” In _Wikipedia_, July 22, 2024. [https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier](https://en.wikipedia.org/w/index.php?title=Uniform_Resource_Identifier&oldid=1235957234).
 <!--ID: 1722212790279-->

notes/set/relations.md

@@ -1091,6 +1091,13 @@ Reference: “Antisymmetric Relation,” in _Wikipedia_, January 24, 2024, [http
 <!--ID: 1721912048142-->
 END%%
 
+%%ANKI
+Cloze
+{1:Distinct} elements is to {2:antisymmetry} whereas {2:any} elements is to {1:asymmetry}.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1722735199608-->
+END%%
+
 ## Transitivity
 
 A relation $R$ is **transitive** iff whenever $xRy$ and $yRz$, then $xRz$. In relational algebra, we define $R$ to be transitive iff $R \circ R \subseteq R$.
@@ -1143,6 +1150,128 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1721694448736-->
 END%%
 
+## Connected
+
+A binary relation $R$ on set $A$ is said to be **connected** if for any *distinct* $x, y \in A$, either $xRy$ or $yRx$. The relation is **strongly connected** if for *all* $x, y \in A$, either $xRy$ or $yRx$.
+
+%%ANKI
+Basic
+How is connectivity of relation $R$ on set $A$ defined in FOL?
+Back: $\forall x, y \in A, x \neq y \Rightarrow xRy \lor yRx$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1722735199628-->
+END%%
+
+%%ANKI
+Basic
+Is $R = \{\langle a, b \rangle\}$ connected on set $\{a, b\}$?
+Back: Yes.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1722735199637-->
+END%%
+
+%%ANKI
+Basic
+Is $R = \{\langle a, a \rangle\}$ connected on set $\{a, b\}$?
+Back: No.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1722735199645-->
+END%%
+
+%%ANKI
+Basic
+*Why* isn't $R = \{\langle a, a \rangle, \langle b, b \rangle\}$ connected on set $\{a, b\}$?
+Back: Because neither $aRb$ nor $bRa$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1722735199650-->
+END%%
+
+%%ANKI
+Basic
+Which of reflexivity or connectivity is the more general concept?
+Back: N/A.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1722735199658-->
+END%%
+
+%%ANKI
+Basic
+What members must be added to make $R = \{\langle a, b \rangle, \langle b, c \rangle, \langle c, a \rangle\}$ connected on $\{a, b, c\}$?
+Back: N/A.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1722735199662-->
+END%%
+
+%%ANKI
+Basic
+How is strong connectivity of relation $R$ on set $A$ defined in FOL?
+Back: $\forall x, y \in A, xRy \lor yRx$
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199672-->
+END%%
+
+%%ANKI
+Basic
+Is $R = \{\langle a, b \rangle\}$ strongly connected on set $\{a, b\}$?
+Back: No.
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199678-->
+END%%
+
+%%ANKI
+Basic
+*Why* isn't $R = \{\langle a, b \rangle\}$ strongly connected on set $\{a, b\}$?
+Back: Because $\neg aRa$ and $\neg bRb$.
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199683-->
+END%%
+
+%%ANKI
+Basic
+What members must be added to make $R = \{\langle a, b \rangle, \langle b, c \rangle, \langle c, a \rangle\}$ strongly connected on $\{a, b, c\}$?
+Back: $\langle a, a \rangle$, $\langle b, b \rangle$, $\langle c, c \rangle$
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199688-->
+END%%
+
+%%ANKI
+Basic
+Which of strong connectivity or reflexivity is the more general concept?
+Back: Reflexivity.
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199695-->
+END%%
+
+%%ANKI
+Cloze
+{1:Antisymmetry} is to {2:asymmetry} as {2:connectivity} is to {1:strong connectivity}.
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199702-->
+END%%
+
+%%ANKI
+Basic
+Why might we say asymmetry is "strong antisymmetry"?
+Back: The former implies the latter.
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199707-->
+END%%
+
+%%ANKI
+Cloze
+{1:Distinct} elements is to {2:connected} whereas {2:any} elements is to {1:strongly connected}.
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199711-->
+END%%
+
+%%ANKI
+Basic
+What makes "strong connectedness" stronger than "connectedness"?
+Back: The former implies the latter.
+Reference: “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+<!--ID: 1722735199715-->
+END%%
+
 ## Equivalence Relations
 
 Given relation $R$ and set $A$, $R$ is an **equivalence relation on $A$** iff $R$ is a binary relation on $A$ that is reflexive on $A$, symmetric, and transitive.
@@ -1615,7 +1744,8 @@ END%%
 
 * “Antisymmetric Relation,” in _Wikipedia_, January 24, 2024, [https://en.wikipedia.org/w/index.php?title=Antisymmetric_relation](https://en.wikipedia.org/w/index.php?title=Antisymmetric_relation&oldid=1198625107).
 * “Asymmetric Relation,” in _Wikipedia_, February 21, 2024, [https://en.wikipedia.org/w/index.php?title=Asymmetric_relation](https://en.wikipedia.org/w/index.php?title=Asymmetric_relation&oldid=1209290822).
-* “Cartesian Product,” in _Wikipedia_, April 17, 2024, [https://en.wikipedia.org/w/index.php?title=Cartesian_product&oldid=1219343305](https://en.wikipedia.org/w/index.php?title=Cartesian_product&oldid=1219343305).
+* “Cartesian Product,” in _Wikipedia_, April 17, 2024, [https://en.wikipedia.org/w/index.php?title=Cartesian_product](https://en.wikipedia.org/w/index.php?title=Cartesian_product&oldid=1219343305).
-* Reference: “Equivalence Relation,” in _Wikipedia_, July 21, 2024, [https://en.wikipedia.org/w/index.php?title=Equivalence_relation](https://en.wikipedia.org/w/index.php?title=Equivalence_relation&oldid=1235801091).
+* “Connected Relation,” in _Wikipedia_, July 14, 2024, [https://en.wikipedia.org/w/index.php?title=Connected_relation](https://en.wikipedia.org/w/index.php?title=Connected_relation&oldid=1234415201).
+* “Equivalence Relation,” in _Wikipedia_, July 21, 2024, [https://en.wikipedia.org/w/index.php?title=Equivalence_relation](https://en.wikipedia.org/w/index.php?title=Equivalence_relation&oldid=1235801091).
 * Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 * “Partition of a Set,” in _Wikipedia_, June 18, 2024, [https://en.wikipedia.org/w/index.php?title=Partition_of_a_set](https://en.wikipedia.org/w/index.php?title=Partition_of_a_set&oldid=1229656401).