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Reorganizing C declarations file.

c-declarations
Joshua Potter 2024-08-04 08:12:40 -06:00
parent 2c099dff15
commit 78c17509bf
8 changed files with 213 additions and 37 deletions
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14
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"fields_dict": { "fields_dict": {
"Basic": [ "Basic": [

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

1
notes/_journal/2024-08-03.md → notes/_journal/2024-08/2024-08-03.md
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@ -9,3 +9,4 @@ title: "2024-08-03"
- [ ] Korean (Read 1 Story) - [ ] Korean (Read 1 Story)
* Additional notes on binary search trees. * Additional notes on binary search trees.
* Notes on (strong) [[relations#Connected|connectivity]] of relations.

2
notes/algebra/set.md
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@ -207,7 +207,7 @@ END%%
%%ANKI %%ANKI
Basic Basic
Assume AoC and $H(j) \neq \varnothing$ for all $j \in I$. What does $\bigtimes_{i \in I} H(i)$ evaluate to? 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). Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1720964209709--> <!--ID: 1720964209709-->
END%% END%%

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notes/c17/declarations.md
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@ -8,6 +8,31 @@ tags:
## Overview ## 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)`
## Declarations
A **declaration** is then at least one type-specifier (e.g. `signed short`), storage class (e.g. `static`), and/or type qualifier (e.g. `const`) followed by one or more declarators.
### Type Specifiers
Signed | Unsigned | 32-bit | 64-bit Signed | Unsigned | 32-bit | 64-bit
----------- | ------------------- | ------ | ------ ----------- | ------------------- | ------ | ------
signed char | unsigned char | 1 | 1 signed char | unsigned char | 1 | 1
@ -415,7 +440,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1714677608769--> <!--ID: 1714677608769-->
END%% END%%
## Pointers ### Pointers
Pointers have the same size as the machine's word size since it should be able to refer to any virtual address. Pointers have the same size as the machine's word size since it should be able to refer to any virtual address.
@ -430,3 +455,4 @@ END%%
## Bibliography ## Bibliography
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. * Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
* Peter Van der Linden and Peter VanDerLinden, _Expert C Programming: Deep C Secrets_, Programming Languages / C (Mountain View, Cal.: SunSoft Pr, 1994).

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notes/combinatorics/permutations.md
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@ -128,12 +128,20 @@ END%%
%%ANKI %%ANKI
Basic 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). 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--> <!--ID: 1708366788603-->
END%% 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 %%ANKI
Basic Basic
What combinatorial concept explains the number of bijective functions between two finite sets? What combinatorial concept explains the number of bijective functions between two finite sets?

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notes/ontology/rdf/uri.md
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@ -162,7 +162,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212201466-->
@ -170,7 +170,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212201450-->
@ -178,23 +178,23 @@ END%%
%%ANKI %%ANKI
Basic 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). 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--> <!--ID: 1722212472982-->
END%% END%%
%%ANKI %%ANKI
Basic 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). 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--> <!--ID: 1722212472988-->
END%% END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212472995-->
@ -202,7 +202,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212201416-->
@ -210,7 +210,7 @@ END%%
%%ANKI %%ANKI
Basic 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. 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). 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--> <!--ID: 1722212201460-->
@ -218,7 +218,7 @@ END%%
%%ANKI %%ANKI
Basic 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. 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). 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--> <!--ID: 1722212201472-->
@ -228,7 +228,7 @@ END%%
Cloze Cloze
The authority of a URI has the following generic syntax: 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). 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--> <!--ID: 1722211744669-->
END%% END%%
@ -251,7 +251,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212473001-->
@ -259,7 +259,7 @@ END%%
%%ANKI %%ANKI
Basic 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. 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). 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--> <!--ID: 1722212790216-->
@ -267,7 +267,7 @@ END%%
%%ANKI %%ANKI
Basic 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]` 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). 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--> <!--ID: 1722212790223-->
@ -275,7 +275,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212790228-->
@ -283,7 +283,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212790232-->
@ -291,7 +291,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212790236-->
@ -299,7 +299,7 @@ END%%
%%ANKI %%ANKI
Basic 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. 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). 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--> <!--ID: 1722212790241-->
@ -307,7 +307,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212790247-->
@ -315,7 +315,7 @@ END%%
%%ANKI %%ANKI
Basic 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. 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). 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--> <!--ID: 1722212790252-->
@ -323,7 +323,7 @@ END%%
%%ANKI %%ANKI
Basic 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. 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). 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--> <!--ID: 1722212790258-->
@ -331,7 +331,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212790265-->
@ -339,7 +339,7 @@ END%%
%%ANKI %%ANKI
Basic 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` 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). 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--> <!--ID: 1722212790272-->
@ -347,7 +347,7 @@ END%%
%%ANKI %%ANKI
Basic 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: `/` 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). 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--> <!--ID: 1722212790279-->

134
notes/set/relations.md
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@ -1091,6 +1091,13 @@ Reference: “Antisymmetric Relation,” in _Wikipedia_, January 24, 2024, [http
<!--ID: 1721912048142--> <!--ID: 1721912048142-->
END%% 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 ## Transitivity
A relation $R$ is **transitive** iff whenever $xRy$ and $yRz$, then $xRz$. In relational algebra, we define $R$ to be transitive iff $R \circ R \subseteq R$. 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--> <!--ID: 1721694448736-->
END%% 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 ## 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. 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). * “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). * “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). * 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). * “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).