Stacks, C declarations, equinumerosity.

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

@@ -219,7 +219,9 @@
     "saved-registers.png",
     "local-variables.png",
     "arg-build-area.png",
-    "stack-frame.png"
+    "stack-frame.png",
+    "buffer-overflow.png",
+    "infinite-cartesian-product.png"
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     "c17/types/enumerated.md": "e1f70a30677c776b7b44ac3e0ff4e76d",
-    "c17/types/derived.md": "26bcaee99aba7720fd76d92e10770933",
+    "c17/types/derived.md": "dcac68790016190ce5c4196bd9c1d53d",
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+    "_journal/2024-11/2024-11-19.md": "d879f57154cb27cb168eb1f1f430e312",
+    "set/cardinality.md": "499e758bc0929af06736fa2974aade60"
   },
   "fields_dict": {
     "Basic": [

notes/_journal/2024-06/2024-06-14.md

@@ -9,4 +9,4 @@ title: "2024-06-14"
 - [ ] Korean (Read 1 Story)
 
 * Finished most notes on [[alpha-conversion|α-conversion]].
-* Starting notes on [[functions]].
+* Starting notes on [[set/functions]].

notes/_journal/2024-06/2024-06-15.md

@@ -8,5 +8,5 @@ title: "2024-06-15"
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 
-* [[functions|Notes]] on injections, surjections, and bijections.
+* [[set/functions|Notes]] on injections, surjections, and bijections.
 * Start defining [[beta-reduction|β-reduction]].

notes/_journal/2024-06/2024-06-21.md

@@ -8,5 +8,5 @@ title: "2024-06-21"
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 
-* Notes on [[functions#Inverses|inverses]] and [[functions#Compositions|compositions]] of functions.
+* Notes on [[set/functions#Inverses|inverses]] and [[set/functions#Compositions|compositions]] of functions.
 * Finished Chapter 8 of "The Science of Programming" on sequential composition.

notes/_journal/2024-06/2024-06-22.md

@@ -10,5 +10,5 @@ title: "2024-06-22"
 
 * Notes on [[beta-reduction#Normal Form|β-normal forms]].
 * Very basic notes on [[abstract-rewriting-systems/index|abstract rewriting systems]].
-* Additional set theory definitions ([[functions#Restrictions|restrictions]] and [[functions#Images|images]]).
+* Additional set theory definitions ([[set/functions#Restrictions|restrictions]] and [[set/functions#Images|images]]).
 * Read chapters 2 ("Methodology") and 3 ("Properties") of "An Introduction to Ontology".

notes/_journal/2024-07/2024-07-17.md

@@ -8,4 +8,4 @@ title: "2024-07-17"
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 
-* Notes on [[relations#Quotient Sets|quotient sets]], function [[functions#Kernels|kernels]], and fibers.
+* Notes on [[relations#Quotient Sets|quotient sets]], function [[set/functions#Kernels|kernels]], and fibers.

notes/_journal/2024-10/2024-10-24.md

@@ -9,5 +9,5 @@ title: "2024-10-24"
 - [ ] Korean (Read 1 Story)
 
 * Finished "Recursion on $\omega$" and "Arithmetic" sections of Enderton's "Elements of Set Theory".
-* Notes on recursively defined [[natural-numbers#Addition|addition]], [[natural-numbers#Multiplication|multiplication]] and [[natural-numbers#Exponentiation|exponentiation]] [[functions|operations]].
+* Notes on recursively defined [[natural-numbers#Addition|addition]], [[natural-numbers#Multiplication|multiplication]] and [[natural-numbers#Exponentiation|exponentiation]] [[set/functions|operations]].
 * Notes on local stack variables and arguments passed on the stack.

notes/_journal/2024-11-22.md

@@ -0,0 +1,13 @@
+---
+title: "2024-11-22"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)
+
+* Read through CS:APP's section "The Y86-64 Instruction Set Architecture".
+* Added notes on the special cases of C's [[c17/declarations#main|main()]] function.
+* Notes on [[cardinality#Overview|equinumerosity]].

notes/_journal/2024-11/2024-11-18.md

@@ -2,9 +2,9 @@
 title: "2024-11-18"
 ---
 
-- [ ] Anki Flashcards
+- [x] Anki Flashcards
 - [x] KoL
-- [ ] OGS
+- [x] OGS
 - [ ] Sheet Music (10 min.)
 - [ ] Korean (Read 1 Story)
 

notes/_journal/2024-11/2024-11-19.md

@@ -0,0 +1,11 @@
+---
+title: "2024-11-19"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)
+
+* [[c17/declarations#Prototypes|Notes]] on prototypes, identifier type lists, and parameter type lists.

notes/_journal/2024-11/2024-11-20.md

@@ -0,0 +1,9 @@
+---
+title: "2024-11-21"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)

notes/_journal/2024-11/2024-11-21.md

@@ -0,0 +1,9 @@
+---
+title: "2024-11-21"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)

notes/algebra/polynomials.md

@@ -87,7 +87,7 @@ END%%
 %%ANKI
 Basic
 What is a binomial?
-Back: A polynomial containing two terms.
+Back: A polynomial containing two non-like terms.
 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: 1708368078759-->
 END%%

notes/algebra/set.md

@@ -905,7 +905,7 @@ END%%
 
 ## Index Sets
 
-Let $I$ be a set, called the **index set**. Let $F$ be a [[functions|function]] whose domain includes $I$. Then we define $$\bigcup_{i \in I} F(i) = \bigcup\,\{F(i) \mid i \in I\}$$
+Let $I$ be a set, called the **index set**. Let $F$ be a [[set/functions|function]] whose domain includes $I$. Then we define $$\bigcup_{i \in I} F(i) = \bigcup\,\{F(i) \mid i \in I\}$$
 and, if $I \neq \varnothing$, $$\bigcap_{i \in I} F(i) = \bigcap\, \{F(i) \mid i \in I\}$$
 
 %%ANKI

notes/c17/declarations.md

@@ -275,6 +275,497 @@ Reference: Van der Linden, Peter. _Expert C Programming: Deep C Secrets_. Progra
 <!--ID: 1722786892125-->
 END%%
 
+## Prototypes
+
+A function declaration/definition has two ways of using declarators: **parameter type lists** and **identifier type lists**. To make the distinction clear, consider the following two ways of defining an `add` function:
+
+```c
+int f(int x, int y) { return x + y; }  // Paramter type list
+int f(x, y) int x; int y; { return x + y }  // Identifier type list
+```
+
+A function **prototype** is a kind of function declaration that specifies the function signature. There are three important points to make note of:
+
+* Empty identifier lists are interpreted as "the compiler has not been told what this function's arguments are."
+* The standard prohibits declaring functions with a non-empty identifier list.
+* Empty parameter lists are not allowed.
+
+Therefore:
+
+```c
+// Uses an empty identifer list. This declares a function `foo`
+// that takes an unknown specification of arguments.
+void foo();
+// Uses a non-empty identifier list. Compiler error.
+void foo(x, y);
+// Uses a non-empty identifier list. Compiler error.
+void foo(x, y) int x; int y;
+// Uses a non-empty identifier list. Definitions allow this.
+void foo(x, y) int x; int y; { }
+// Uses a non-empty parameter list. This prototypes a function
+// `foo` that takes no arguments.
+void foo(void);
+// Uses a non-empty parameter list. This prototypes and defines
+// a function `foo` that takes no arguments.
+void foo(void) {}
+```
+
+Together these points imply a function prototype *must* use a parameter type list.
+
+%%ANKI
+Basic
+Which of prototypes or declarations are more general?
+Back: Declarations.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751462-->
+END%%
+
+%%ANKI
+Basic
+What two ways are parameters declared in function declarations and definitions?
+Back: Identifier type lists and parameter type lists.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751467-->
+END%%
+
+%%ANKI
+Basic
+Which of identifier type lists and/or parameter type lists considered obsolete?
+Back: Identifier type lists.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751470-->
+END%%
+
+%%ANKI
+Basic
+Define an addition function using identifier type lists.
+Back:
+```c
+int add(x, y) int x; int y; { return x + y; }
+```
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751473-->
+END%%
+
+%%ANKI
+Basic
+Define an addition function using parameter type lists.
+Back:
+```c
+int add(int x, int y) { return x + y; }
+```
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751476-->
+END%%
+
+%%ANKI
+Basic
+Is the following a prototype or a declaration?
+```c
+void foo();
+```
+Back: A declaration.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751479-->
+END%%
+
+%%ANKI
+Basic
+What compilation error does the following raise?
+```c
+void foo();
+```
+Back: N/A.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751482-->
+END%%
+
+%%ANKI
+Basic
+What compilation error does the following raise?
+```c
+void foo(x, y);
+```
+Back: A function declaration cannot have a non-empty identifier list.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751486-->
+END%%
+
+%%ANKI
+Basic
+What compilation error does the following raise?
+```c
+void foo(x, y) int x; int y;
+```
+Back: A function declaration cannot have a non-empty identifier list.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751490-->
+END%%
+
+%%ANKI
+Basic
+What compilation error does the following raise?
+```c
+void foo(x, y) int x; int y; {}
+```
+Back: N/A.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751495-->
+END%%
+
+%%ANKI
+Basic
+What function prototype is declared in the following?
+```c
+void foo(x, y) int x; int y; {}
+```
+Back: N/A. No prototype has been declared.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751499-->
+END%%
+
+%%ANKI
+Basic
+What compilation error does the following raise?
+```c
+void foo();
+
+int main(void) { foo(1); }
+```
+Back: N/A.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751504-->
+END%%
+
+%%ANKI
+Basic
+Is the following a prototype or a declaration?
+```c
+void f(void);
+```
+Back: A prototype.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751509-->
+END%%
+
+%%ANKI
+Basic
+What compilation error does the following raise?
+```c
+void foo(void);
+```
+Back: N/A.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751513-->
+END%%
+
+%%ANKI
+Basic
+What compilation error does the following raise?
+```c
+void foo(void);
+
+int main(void) { foo(1); }
+```
+Back: Too many arguments to function call `foo`.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751518-->
+END%%
+
+%%ANKI
+Basic
+What function prototype is declared in the following?
+```c
+void foo(int x, int y);
+```
+Back: `void foo(int, int)`
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751522-->
+END%%
+
+%%ANKI
+Basic
+What function prototype is declared in the following?
+```c
+void foo(int x, int y) {}
+```
+Back: `void foo(int, int)`
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751527-->
+END%%
+
+%%ANKI
+Basic
+How many arguments does the following declaration specify?
+```c
+void foo();
+```
+Back: Some number unknown to the compiler.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751531-->
+END%%
+
+%%ANKI
+Basic
+How many arguments does the following declaration specify?
+```c
+void foo(void);
+```
+Back: Zero.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751535-->
+END%%
+
+%%ANKI
+Basic
+Why might the following snippet raise a compilation error?
+```c
+int foo();
+int foo(int a);
+```
+Back: N/A. It likely wouldn't.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751539-->
+END%%
+
+%%ANKI
+Basic
+*Why* might the following snippet raise a compilation error?
+```c
+int foo();
+int foo(float a);
+```
+Back: Conflicting types. The first `foo` declares any `float` passed to it default promotes to a `double`.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751543-->
+END%%
+
+%%ANKI
+Basic
+*Why* might the following snippet raise a compilation error?
+```c
+int foo();
+int foo(char a);
+```
+Back: Conflicting types. The first `foo` declares any `char` passed to it default promotes to an `int`.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751547-->
+END%%
+
+%%ANKI
+Basic
+*Why* might the following snippet raise a compilation error?
+```c
+int foo();
+int foo(double a);
+```
+Back: N/A. It likely wouldn't.
+Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70.net/~nsz/c/c11/n1570.pdf](https://port70.net/~nsz/c/c11/n1570.pdf).
+<!--ID: 1732031751552-->
+END%%
+
+### main
+
+`main` is a special function serving as the entrypoint to C programs. It can have several different prototypes, but the following two are always possible:
+
+```c
+int main(void);
+int main(int argc, char* argv[argc+1]);
+```
+
+The only two return values guaranteed to work on all platform is `EXIT_SUCCESS` and `EXIT_FAILURE`. Reaching the end of `main` is equivalent to a `reutrn` with value `EXIT_SUCCESS`.
+
+%%ANKI
+Basic
+Which function serves as the entrypoint of C programs?
+Back: `main`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415792-->
+END%%
+
+%%ANKI
+Basic
+How many valid prototypes of `main` are available?
+Back: Indeterminate. Depends on the system.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415798-->
+END%%
+
+%%ANKI
+Basic
+How many "official" prototypes of `main` are available?
+Back: Two.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415801-->
+END%%
+
+%%ANKI
+Basic
+What are the "official" prototypes of `main`?
+Back:
+```c
+int main(void);
+int main(int argc, char* argv[argc + 1]);
+```
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415804-->
+END%%
+
+%%ANKI
+Basic
+What are the "official" prototypes of `main`?
+Back:
+```c
+int main(void);
+int main(int argc, char* argv[argc + 1]);
+```
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+END%%
+
+%%ANKI
+Basic
+What are the only portable values that `main` can return?
+Back: `EXIT_SUCCESS` and `EXIT_FAILURE`.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415807-->
+END%%
+
+%%ANKI
+Basic
+Which library defines `EXIT_SUCCESS`?
+Back: `stdlib.h`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415810-->
+END%%
+
+%%ANKI
+Basic
+Which library defines `EXIT_FAILURE`?
+Back: `stdlib.h`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415813-->
+END%%
+
+%%ANKI
+Basic
+What happens when `main` does not explicitly return a value?
+Back: `EXIT_SUCCESS` is implicitly returned.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415816-->
+END%%
+
+%%ANKI
+Cloze
+Returning {1:`s`} in {1:`main`} is equivalent to invoking function {2:`exit`} with argument {2:`s`}.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415819-->
+END%%
+
+%%ANKI
+Basic
+Which library declares the following prototype?
+```c
+noreturn void exit(int)
+```
+Back: `stdlib.h`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415823-->
+END%%
+
+%%ANKI
+Basic
+What does keyword `_Noreturn` indicate?
+Back: The associated callee will never return control back to the caller.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415827-->
+END%%
+
+%%ANKI
+Basic
+What kind of syntactical construct is `_Noreturn`?
+Back: A special keyword.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415832-->
+END%%
+
+%%ANKI
+Basic
+What kind of syntactical construct is `noreturn`?
+Back: A macro.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415836-->
+END%%
+
+%%ANKI
+Cloze
+{1:`_Noreturn`} is a {2:keyword} whereas {2:`noreturn`} is a {1:macro}.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415841-->
+END%%
+
+%%ANKI
+Basic
+Which library is `noreturn` defined in?
+Back: `stdnoreturn.h`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415846-->
+END%%
+
+%%ANKI
+Basic
+Consider the following prototype. What is the value of `argv[0]`?
+```c
+int main(int argc, char* argv[argc + 1]);
+```
+Back: The name of the program invocation.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415851-->
+END%%
+
+%%ANKI
+Basic
+Consider the following prototype. What is the value of `argv[argc]`?
+```c
+int main(int argc, char* argv[argc + 1]);
+```
+Back: `0`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415856-->
+END%%
+
+%%ANKI
+Basic
+Consider the following prototype. What is the value of `argv[1]`?
+```c
+int main(int argc, char* argv[argc + 1]);
+```
+Back: `0` if `argc == 1` else the first argument to the program.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415860-->
+END%%
+
+%%ANKI
+Basic
+Consider the following prototype. What is the minimum value of `argc`?
+```c
+int main(int argc, char* argv[argc + 1]);
+```
+Back: `1`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415865-->
+END%%
+
+%%ANKI
+Basic
+Consider the following prototype. What is the minimum length of `argv`?
+```c
+int main(int argc, char* argv[argc + 1]);
+```
+Back: `2`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1732293415869-->
+END%%
+
 ## Initializers
 
 An **initializer** is an expression that gives an object a value at time of declaration. Only variable-length arrays (VLAs) do not allow for an initializer. The default initializer looks like `{0}`.

notes/c17/strings.md

@@ -84,6 +84,33 @@ Tags: printf
 <!--ID: 1708974221761-->
 END%%
 
+%%ANKI
+Basic
+What is the purpose of the width field in a `printf` argument?
+Back: It specifies a minimum number of characters to ouput.
+Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
+Tags: printf
+<!--ID: 1732285301746-->
+END%%
+
+%%ANKI
+Basic
+What is the purpose of the precision field in a `printf` argument?
+Back: It specifies the maximum limit on the output, depending on the argument type.
+Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
+Tags: printf
+<!--ID: 1732285301754-->
+END%%
+
+%%ANKI
+Basic
+What is the purpose of the length field in a `printf` argument?
+Back: It specifies the size of the `printf` argument before default promotion.
+Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
+Tags: printf
+<!--ID: 1732285301762-->
+END%%
+
 %%ANKI
 Basic
 Which header file contains basic `printf` functionality?

notes/c17/types/derived.md

@@ -563,8 +563,8 @@ END%%
 Basic
 *Why* must FLAs be declared within a function?
 Back: N/A. They can exist elsewhere.
-Tags: x86-64
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: x86-64
 <!--ID: 1731952634167-->
 END%%
 
@@ -592,8 +592,8 @@ END%%
 Basic
 *Why* do variable-length arrays require use of a frame pointer?
 Back: Offsets depend on how much space must be allocated on the stack.
-Tags: x86-64
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: x86-64
 <!--ID: 1731952634169-->
 END%%
 
@@ -601,8 +601,8 @@ END%%
 Basic
 *Why* must VLAs be declared within a function?
 Back: Their implementation relies on frame pointers.
-Tags: x86-64
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: x86-64
 <!--ID: 1731952634170-->
 END%%
 

notes/set/cardinality.md

@@ -0,0 +1,148 @@
+---
+title: Cardinality
+TARGET DECK: Obsidian::STEM
+FILE TAGS: set::cardinality
+tags:
+  - set
+---
+
+## Overview
+
+We say set $A$ is **equinumerous** to set $B$, written ($A \approx B$) if and only if there exists a [[functions#Injections|one-to-one]] function from $A$ [[functions#Surjections|onto]] $B$.
+
+%%ANKI
+Basic
+Suppose $A$ is equinumerous to $B$. How does Enderton denote this?
+Back: $A \approx B$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060344-->
+END%%
+
+%%ANKI
+Basic
+What does it mean for $A$ to be equinumerous to $B$?
+Back: There exists a bijection between $A$ and $B$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060352-->
+END%%
+
+%%ANKI
+Basic
+Suppose $A \approx B$. Then what must exist?
+Back: A bijection between $A$ and $B$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060355-->
+END%%
+
+%%ANKI
+Basic
+Suppose there exists a one-to-one function $F$ from $A$ into $B$. When is $A \approx B$?
+Back: When $F$ is also onto $B$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060358-->
+END%%
+
+%%ANKI
+Basic
+Suppose there exists a function $F$ from $A$ onto $B$. When is $A \approx B$?
+Back: When $F$ is also one-to-one.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060362-->
+END%%
+
+%%ANKI
+Basic
+Suppose there exists a one-to-one function $F$ from $A$ onto $B$. When is $A \approx B$?
+Back: Always, by definition.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060366-->
+END%%
+
+## Equivalence Concept
+
+For any sets $A$, $B$, and $C$:
+
+* $A \approx A$;
+* if $A \approx B$, then $B \approx A$;
+* if $A \approx B$ and $B \approx C$, then $A \approx C$.
+
+Notice though that $\{ \langle A, B \rangle \mid A \approx B \}$ is *not* an equivalence relation since the equivalence concept of equinumerosity concerns *all* sets.
+
+%%ANKI
+Basic
+Concisely state the equivalence concept of equinumerosity in Zermelo-Fraenkel set theory.
+Back: For all sets $A$, $B$, and $C$:
+* $A \approx A$;
+* $A \approx B \Rightarrow B \approx A$;
+* $A \approx B \land B \approx C \Rightarrow A \approx C$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060370-->
+END%%
+
+%%ANKI
+Basic
+Concisely state the equivalence concept of equinumerosity in von Neumann-Bernays set theory.
+Back: Class $\{ \langle A, B \rangle \mid A \approx B \}$ is reflexive on the class of all sets, symmetric, and transitive.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060374-->
+END%%
+
+%%ANKI
+Basic
+What is the reflexive property of equinumerosity in FOL?
+Back: $\forall A, A \approx A$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060379-->
+END%%
+
+%%ANKI
+Basic
+What is the symmetric property of equinumerosity in FOL?
+Back: $\forall A, B, A \approx B \Rightarrow B \approx A$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060383-->
+END%%
+
+%%ANKI
+Basic
+What is the transitive property of equinumerosity in FOL?
+Back: $\forall A, B, C, A \approx B \land B \approx C \Rightarrow A \approx C$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060387-->
+END%%
+
+%%ANKI
+Basic
+Is $\{ \langle A, B \rangle \mid A \approx B \}$ a set?
+Back: No.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060390-->
+END%%
+
+%%ANKI
+Basic
+*Why* isn't $\{ \langle A, B \rangle \mid A \approx B \}$ a set?
+Back: Because then the field of this "relation" would be a set.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060394-->
+END%%
+
+%%ANKI
+Basic
+Is $\{ \langle A, B \rangle \mid A \approx B \}$ an equivalence relation?
+Back: No.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060398-->
+END%%
+
+%%ANKI
+Basic
+*Why* isn't $\{ \langle A, B \rangle \mid A \approx B \}$ an equivalence relation?
+Back: Because then the field of this "relation" would be a set.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1732295060403-->
+END%%
+
+## Bibliography
+
+* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).

notes/x86-64/instructions/procedures.md

@@ -152,7 +152,7 @@ END%%
 %%ANKI
 Basic
 Variable-sized frames use which of `leave` and/or `ret`?
-Back: Bot
+Back: Both.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1731952715103-->
 END%%

notes/x86-64/procedures.md

@@ -585,7 +585,7 @@ END%%
 
 %%ANKI
 Cloze
-By convention, register `%rbp` is used for {callee-saved values}.
+By convention, register `%rbp` is used for {base pointers}.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1730121604421-->
 END%%
@@ -683,8 +683,8 @@ END%%
 
 %%ANKI
 Basic
-When is the `%rbp` register used?
+What kind of frames use the `%rbp` register?
-Back: When working with variable-sized frames.
+Back: Variable-sized frames.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1731952634153-->
 END%%
@@ -753,6 +753,23 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1731952634161-->
 END%%
 
+%%ANKI
+Basic
+Allocate an array in a stack frame. Is the start of the array nearer the stack's top or bottom?
+Back: Bottom.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1732025483593-->
+END%%
+
+%%ANKI
+Basic
+Suppose an array exists in "Local variables". What region is trampled in a buffer overflow?
+![[buffer-overflow.png]]
+Back: The return address.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1732025483600-->
+END%%
+
 ## Bibliography
 
 * Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.