diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index cf29fed..2940f71 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -254,7 +254,7 @@ "combinatorics/additive-principle.md": "d036ac511e382d5c1caca437341a5915", "_journal/2024-02-19.md": "30d16c5373deb9cb128d2e7934ae256a", "_journal/2024-02/2024-02-18.md": "67e36dbbb2cac699d4533b5a2eaeb629", - "combinatorics/permutations.md": "efd0820ab3cc7faa5b2df3fe40105110", + "combinatorics/permutations.md": "f2f3188f4e1142ec39de1e44ac5a1f0a", "combinatorics/combinations.md": "396fc32255710eaf33213efaafdc43d4", "_journal/2024-02-20.md": "b85ba0eeeb16e30a602ccefabcc9763e", "_journal/2024-02/2024-02-19.md": "df1a9ab7ab89244021b3003c84640c78", @@ -495,7 +495,7 @@ "_journal/2024-05/2024-05-25.md": "3e8a0061fa58a6e5c48d12800d1ab869", "_journal/2024-05-27.md": "b36636d10eab34380f17f288868df3ae", "_journal/2024-05/2024-05-26.md": "abe84b5beae74baa25501c818e64fc95", - "algebra/set.md": "b4d5ce4b914abe5063bf6043cf7a0aee", + "algebra/set.md": "30a13f1db3c53dbff179eca2873d7732", "algebra/boolean.md": "fc47edb7d0080b73ce1ce0d3e0e16d7d", "git/merge-conflicts.md": "761ad6137ec51d3877f7d5b3615ca5cb", "_journal/2024-05-28.md": "0f6aeb5ec126560acdc2d8c5c6570337", @@ -520,7 +520,7 @@ "_journal/2024-06/2024-06-04.md": "52b28035b9c91c9b14cef1154c1a0fa1", "_journal/2024-06-06.md": "3f9109925dea304e7172df39922cc95a", "_journal/2024-06/2024-06-05.md": "b06a0fa567bd81e3b593f7e1838f9de1", - "set/relations.md": "84a66a74805014d3b88ea5e8a3e763bc", + "set/relations.md": "9f59faf0f21dfe49ad89ac6e8115d269", "_journal/2024-06-07.md": "795be41cc3c9c0f27361696d237604a2", "_journal/2024-06/2024-06-06.md": "db3407dcc86fa759b061246ec9fbd381", "_journal/2024-06-08.md": "b20d39dab30b4e12559a831ab8d2f9b8", @@ -659,7 +659,7 @@ "_journal/2024-07/2024-07-26.md": "c167f734a5037e1a5537b1e95ca6790f", "_journal/2024-07-28.md": "8a2393673132ac57a86b3b528bfc4a16", "_journal/2024-07/2024-07-27.md": "7c48690746d8320494e29e92390eb6ee", - "ontology/rdf/uri.md": "07999207f65ffb35f55af42c9922e7c5", + "ontology/rdf/uri.md": "7dde3e92eee17ea85e75df3fdc5f8d51", "ontology/rdf/index.md": "36424c9bad6088cdee67f74e3b8a019f", "ontology/philosophy/permissivism.md": "643e815a79bc5c050cde9f996aa44ef5", "ontology/philosophy/nominalism.md": "46245c644238157e15c7cb6def27d90a", @@ -674,9 +674,11 @@ "_journal/2024-07/2024-07-31.md": "d397c5a4d42660eeaa290aa8316d55c1", "_journal/2024-07/2024-07-30.md": "025194b9b770b56a81b5a52d96a305f2", "_journal/2024-08-02.md": "24648f61c675c1c52e4cb19cbac6f0dc", - "_journal/2024-08-03.md": "27f1316f792f7673cd7ea1b1e44444be", + "_journal/2024-08-03.md": "1afbd61dac3039aa3637a9c472813d67", "_journal/2024-08/2024-08-02.md": "076c35545f292eddd3c7253a41fbd40c", - "_journal/2024-08/2024-08-01.md": "2e3da352cfbaf29b6b49e3c3a4f090df" + "_journal/2024-08/2024-08-01.md": "2e3da352cfbaf29b6b49e3c3a4f090df", + "_journal/2024-08-04.md": "259c22c25de23166f0554b2c971255fd", + "_journal/2024-08/2024-08-03.md": "7c1d3dbaf47d1120bb879110e827d1b3" }, "fields_dict": { "Basic": [ diff --git a/notes/_journal/2024-08-04.md b/notes/_journal/2024-08-04.md new file mode 100644 index 0000000..aa5e1c0 --- /dev/null +++ b/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) \ No newline at end of file diff --git a/notes/_journal/2024-08-03.md b/notes/_journal/2024-08/2024-08-03.md similarity index 53% rename from notes/_journal/2024-08-03.md rename to notes/_journal/2024-08/2024-08-03.md index 9194ff6..c4c525c 100644 --- a/notes/_journal/2024-08-03.md +++ b/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. \ No newline at end of file +* Additional notes on binary search trees. +* Notes on (strong) [[relations#Connected|connectivity]] of relations. \ No newline at end of file diff --git a/notes/algebra/set.md b/notes/algebra/set.md index f4c353b..bd0f515 100644 --- a/notes/algebra/set.md +++ b/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). END%% diff --git a/notes/c17/declarations.md b/notes/c17/declarations.md index 04e2ca7..ec0ccda 100644 --- a/notes/c17/declarations.md +++ b/notes/c17/declarations.md @@ -8,6 +8,31 @@ 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)` + +## 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 char | unsigned char | 1 | 1 @@ -415,7 +440,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program 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. @@ -430,3 +455,4 @@ END%% ## Bibliography * 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). diff --git a/notes/combinatorics/permutations.md b/notes/combinatorics/permutations.md index 2ca5765..96359ff 100644 --- a/notes/combinatorics/permutations.md +++ b/notes/combinatorics/permutations.md @@ -128,12 +128,20 @@ END%% %%ANKI Basic -*Why* might $0! = 1$ (barring convention)? -Back: Because the empty product is $1$, the multiplication identity. +How is the multiplication identity used to justify equality $0! = 1$? +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). 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). + +END%% + %%ANKI Basic What combinatorial concept explains the number of bijective functions between two finite sets? diff --git a/notes/ontology/rdf/uri.md b/notes/ontology/rdf/uri.md index d3d4616..60a5843 100644 --- a/notes/ontology/rdf/uri.md +++ b/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). @@ -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). @@ -178,23 +178,23 @@ END%% %%ANKI Basic -The following URI has what userinfo? $$\text{http://www.example.com/questions/3456/my-document}$$ -Back: N/A. It is undefined +The following URI specifies what userinfo? $$\text{http://www.example.com/questions/3456/my-document}$$ +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). END%% %%ANKI Basic -The following URI has what port? $$\text{http://www.example.com/questions/3456/my-document}$$ -Back: N/A. It is undefined +The following URI specifies what port? $$\text{http://www.example.com/questions/3456/my-document}$$ +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). 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). @@ -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). @@ -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). @@ -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). @@ -228,7 +228,7 @@ END%% Cloze The authority of a URI has the following generic syntax: -{`[@]`}{``}{`[:]} +{`[@]`}{``}{`[:]`} 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). 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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). @@ -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). diff --git a/notes/set/relations.md b/notes/set/relations.md index fe1838b..a9726d1 100644 --- a/notes/set/relations.md +++ b/notes/set/relations.md @@ -1091,6 +1091,13 @@ Reference: “Antisymmetric Relation,” in _Wikipedia_, January 24, 2024, [http 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). + +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 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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). + +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). -* 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). +* “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). +* “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). \ No newline at end of file