Reorganizing C declarations file.
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@ -254,7 +254,7 @@
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"combinatorics/additive-principle.md": "d036ac511e382d5c1caca437341a5915",
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"_journal/2024-02-19.md": "30d16c5373deb9cb128d2e7934ae256a",
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"_journal/2024-02/2024-02-18.md": "67e36dbbb2cac699d4533b5a2eaeb629",
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"combinatorics/permutations.md": "efd0820ab3cc7faa5b2df3fe40105110",
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"combinatorics/permutations.md": "f2f3188f4e1142ec39de1e44ac5a1f0a",
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"combinatorics/combinations.md": "396fc32255710eaf33213efaafdc43d4",
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"_journal/2024-02-20.md": "b85ba0eeeb16e30a602ccefabcc9763e",
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"_journal/2024-02/2024-02-19.md": "df1a9ab7ab89244021b3003c84640c78",
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@ -495,7 +495,7 @@
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"_journal/2024-05/2024-05-25.md": "3e8a0061fa58a6e5c48d12800d1ab869",
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"_journal/2024-05-27.md": "b36636d10eab34380f17f288868df3ae",
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"_journal/2024-05/2024-05-26.md": "abe84b5beae74baa25501c818e64fc95",
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"algebra/set.md": "b4d5ce4b914abe5063bf6043cf7a0aee",
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"algebra/set.md": "30a13f1db3c53dbff179eca2873d7732",
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"algebra/boolean.md": "fc47edb7d0080b73ce1ce0d3e0e16d7d",
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"git/merge-conflicts.md": "761ad6137ec51d3877f7d5b3615ca5cb",
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"_journal/2024-05-28.md": "0f6aeb5ec126560acdc2d8c5c6570337",
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@ -520,7 +520,7 @@
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"_journal/2024-06/2024-06-04.md": "52b28035b9c91c9b14cef1154c1a0fa1",
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"_journal/2024-06-06.md": "3f9109925dea304e7172df39922cc95a",
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"_journal/2024-06/2024-06-05.md": "b06a0fa567bd81e3b593f7e1838f9de1",
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"set/relations.md": "84a66a74805014d3b88ea5e8a3e763bc",
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"set/relations.md": "9f59faf0f21dfe49ad89ac6e8115d269",
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"_journal/2024-06-07.md": "795be41cc3c9c0f27361696d237604a2",
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"_journal/2024-06/2024-06-06.md": "db3407dcc86fa759b061246ec9fbd381",
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"_journal/2024-06-08.md": "b20d39dab30b4e12559a831ab8d2f9b8",
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@ -659,7 +659,7 @@
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"_journal/2024-07/2024-07-26.md": "c167f734a5037e1a5537b1e95ca6790f",
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"_journal/2024-07-28.md": "8a2393673132ac57a86b3b528bfc4a16",
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"_journal/2024-07/2024-07-27.md": "7c48690746d8320494e29e92390eb6ee",
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"ontology/rdf/uri.md": "07999207f65ffb35f55af42c9922e7c5",
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"ontology/rdf/uri.md": "7dde3e92eee17ea85e75df3fdc5f8d51",
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"ontology/rdf/index.md": "36424c9bad6088cdee67f74e3b8a019f",
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"ontology/philosophy/permissivism.md": "643e815a79bc5c050cde9f996aa44ef5",
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"ontology/philosophy/nominalism.md": "46245c644238157e15c7cb6def27d90a",
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@ -674,9 +674,11 @@
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"_journal/2024-07/2024-07-31.md": "d397c5a4d42660eeaa290aa8316d55c1",
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"_journal/2024-07/2024-07-30.md": "025194b9b770b56a81b5a52d96a305f2",
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"_journal/2024-08-02.md": "24648f61c675c1c52e4cb19cbac6f0dc",
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"_journal/2024-08-03.md": "27f1316f792f7673cd7ea1b1e44444be",
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"_journal/2024-08-03.md": "1afbd61dac3039aa3637a9c472813d67",
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"_journal/2024-08/2024-08-02.md": "076c35545f292eddd3c7253a41fbd40c",
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"_journal/2024-08/2024-08-01.md": "2e3da352cfbaf29b6b49e3c3a4f090df"
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"_journal/2024-08/2024-08-01.md": "2e3da352cfbaf29b6b49e3c3a4f090df",
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"_journal/2024-08-04.md": "259c22c25de23166f0554b2c971255fd",
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"_journal/2024-08/2024-08-03.md": "7c1d3dbaf47d1120bb879110e827d1b3"
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},
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"fields_dict": {
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"Basic": [
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@ -0,0 +1,9 @@
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---
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title: "2024-08-04"
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---
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- [x] Anki Flashcards
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- [x] KoL
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- [x] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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@ -9,3 +9,4 @@ title: "2024-08-03"
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- [ ] Korean (Read 1 Story)
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* Additional notes on binary search trees.
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* Notes on (strong) [[relations#Connected|connectivity]] of relations.
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@ -207,7 +207,7 @@ END%%
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%%ANKI
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Basic
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Assume AoC and $H(j) \neq \varnothing$ for all $j \in I$. What does $\bigtimes_{i \in I} H(i)$ evaluate to?
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Back: A non-empty set.
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Back: $\{f \mid f \text{ is a function with domain } I \text{ and } \forall i \in I, f(i) \in H(i)\}$
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1720964209709-->
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END%%
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@ -8,6 +8,31 @@ tags:
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## Overview
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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.
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## Declarators
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A **declarator** in C is roughly an identifier along with pointers, function brackets, or array indications. Pointers will look like one of:
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* `*`
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* `* const`
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* `* volatile`
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* `* const volatile`
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* `* volatile const`
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whereas **direct declarators** will look like one of:
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* `identifier`
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* `identifier[size]`
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* `identifier(args)`
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* `(declarator)`
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## Declarations
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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.
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### Type Specifiers
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Signed | Unsigned | 32-bit | 64-bit
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----------- | ------------------- | ------ | ------
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signed char | unsigned char | 1 | 1
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@ -415,7 +440,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
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<!--ID: 1714677608769-->
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END%%
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## Pointers
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### Pointers
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Pointers have the same size as the machine's word size since it should be able to refer to any virtual address.
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@ -430,3 +455,4 @@ END%%
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## Bibliography
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* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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* 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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@ -128,12 +128,20 @@ END%%
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%%ANKI
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Basic
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*Why* might $0! = 1$ (barring convention)?
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Back: Because the empty product is $1$, the multiplication identity.
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How is the multiplication identity used to justify equality $0! = 1$?
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Back: The empty product is $1$, i.e. the multiplication identity.
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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).
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<!--ID: 1708366788603-->
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END%%
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%%ANKI
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Basic
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What combinatorial explanation justifies equality $0! = 1$?
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Back: There is only $1$ way to order $0$ objects.
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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).
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<!--ID: 1722775277862-->
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END%%
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%%ANKI
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Basic
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What combinatorial concept explains the number of bijective functions between two finite sets?
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@ -162,7 +162,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what scheme? $$\text{http://www.example.com/questions/3456/my-document}$$
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The following URI specifies what scheme? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: `http`
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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).
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<!--ID: 1722212201466-->
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@ -170,7 +170,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what authority? $$\text{http://www.example.com/questions/3456/my-document}$$
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The following URI specifies what authority? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: `//www.example.com`
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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).
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<!--ID: 1722212201450-->
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@ -178,23 +178,23 @@ END%%
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%%ANKI
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Basic
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The following URI has what userinfo? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: N/A. It is undefined
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The following URI specifies what userinfo? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: N/A. It is undefined.
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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).
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<!--ID: 1722212472982-->
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END%%
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%%ANKI
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Basic
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The following URI has what port? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: N/A. It is undefined
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The following URI specifies what port? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: N/A. It is undefined.
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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).
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<!--ID: 1722212472988-->
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END%%
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%%ANKI
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Basic
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The following URI has what host? $$\text{http://www.example.com/questions/3456/my-document}$$
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The following URI specifies what host? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: `www.example.com`
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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).
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<!--ID: 1722212472995-->
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@ -202,7 +202,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what path? $$\text{http://www.example.com/questions/3456/my-document}$$
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The following URI specifies what path? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: `/questions/3456/my-document`
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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).
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<!--ID: 1722212201416-->
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@ -210,7 +210,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what query? $$\text{http://www.example.com/questions/3456/my-document}$$
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The following URI specifies what query? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: N/A. It is undefined.
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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).
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<!--ID: 1722212201460-->
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@ -218,7 +218,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what fragment? $$\text{http://www.example.com/questions/3456/my-document}$$
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The following URI specifies what fragment? $$\text{http://www.example.com/questions/3456/my-document}$$
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Back: N/A. It is undefined.
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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).
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<!--ID: 1722212201472-->
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@ -228,7 +228,7 @@ END%%
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Cloze
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The authority of a URI has the following generic syntax:
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{`[<userinfo>@]`}{`<host>`}{`[:<port>]}
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{`[<userinfo>@]`}{`<host>`}{`[:<port>]`}
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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).
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<!--ID: 1722211744669-->
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END%%
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@ -251,7 +251,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what fragment? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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The following URI specifies what scheme? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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Back: `ldap`
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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).
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<!--ID: 1722212473001-->
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@ -259,7 +259,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what fragment? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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The following URI specifies what fragment? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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Back: N/A. It is undefined.
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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).
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<!--ID: 1722212790216-->
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@ -267,7 +267,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what authority? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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The following URI specifies what authority? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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Back: `[2001:db8::7]`
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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).
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<!--ID: 1722212790223-->
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@ -275,7 +275,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what query? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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The following URI specifies what query? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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Back: `objectClass?one`
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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).
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<!--ID: 1722212790228-->
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@ -283,7 +283,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what path? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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The following URI specifies what path? $$\text{ldap://[2001:db8::7]/c=GB?objectClass?one}$$
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Back: `/c=GB`
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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).
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<!--ID: 1722212790232-->
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@ -291,7 +291,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what scheme? $$\text{tel:+1-816-555-1212}$$
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The following URI specifies what scheme? $$\text{tel:+1-816-555-1212}$$
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Back: `tel`
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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).
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<!--ID: 1722212790236-->
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@ -299,7 +299,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what authority? $$\text{tel:+1-816-555-1212}$$
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The following URI specifies what authority? $$\text{tel:+1-816-555-1212}$$
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Back: N/A. It is undefined.
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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).
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<!--ID: 1722212790241-->
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@ -307,7 +307,7 @@ END%%
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%%ANKI
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Basic
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The following URI has what path? $$\text{tel:+1-816-555-1212}$$
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The following URI specifies what path? $$\text{tel:+1-816-555-1212}$$
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Back: `+1-816-555-1212`
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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).
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<!--ID: 1722212790247-->
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@ -315,7 +315,7 @@ END%%
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%%ANKI
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Basic
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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-->
|
||||
|
|
|
|||
|
|
@ -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).
|
||||
* 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).
|
||||
Loading…
Reference in New Issue