More cardinality related notes.

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

@@ -939,7 +939,7 @@
     "_journal/2024-10/2024-10-31.md": "8c5e70f566953974f252da9472e527f0",
     "_journal/2024-10/2024-10-30.md": "054bdbf52843fa2445f6b9f91d5ca46e",
     "_journal/2024-10/2024-10-29.md": "432b3b073dafd54421ff6f7182ab9a58",
-    "c17/alignment.md": "bda6444de141aeb8072d3ef2971c4d30",
+    "c17/alignment.md": "a1c0e0ad05827beba761f79b7105eedd",
     "_journal/2024-11-05.md": "6a599e6bc9dcd12a0940956285ae4d00",
     "_journal/2024-11-06.md": "c91de8a099cfee2514e1054400996e76",
     "_journal/2024-11/2024-11-05.md": "79a1304037e18fefa135d576db040784",
@@ -970,7 +970,7 @@
     "_journal/2024-11/2024-11-21.md": "951b6034d60a40dbd8201c50abf0dbb9",
     "_journal/2024-11/2024-11-20.md": "951b6034d60a40dbd8201c50abf0dbb9",
     "_journal/2024-11/2024-11-19.md": "d879f57154cb27cb168eb1f1f430e312",
-    "set/cardinality.md": "cbd0d738ab8b1131f8db0aa23f1ea894",
+    "set/cardinality.md": "d064d5e50586ef6794845c3e39f3c7e1",
     "geometry/area.md": "7f947bb5ac782495a1fb4a63bb2463e7",
     "_journal/2024-11-23.md": "911f82ab8aede5ecdb96493aef64b0b9",
     "_journal/2024-11/2024-11-22.md": "51117030e2364dbce3a8d507dead86ae",
@@ -981,12 +981,12 @@
     "_journal/2024-11-26.md": "29bc0b54d23034b9108e567a1d5fa8ac",
     "_journal/2024-11/2024-11-25.md": "1ec17a8473fa9c4779090ecbd22d70ef",
     "calculus/intervals.md": "163f636be5d9f61ae675b9619408e4c6",
-    "c17/storage.md": "528d7409c1c0298baf9bb55738699f47",
+    "c17/storage.md": "6e300ead477e62c1c726dd7b5e73d7c2",
     "c17/functions.md": "76b12732875998c44b22ba3531cf88a0",
     "_journal/2024-11-27.md": "5a58e3a0bd08c689d30600021937495d",
     "_journal/2024-11/2024-11-26.md": "af7573eb695b61106e04c9f1aee51cc3",
     "_journal/2024-11-28.md": "4321856aec890b179f1b569b908bba60",
-    "c17/linkage.md": "1e4f60f07619b9cbf2f71f11aae9e5f4",
+    "c17/linkage.md": "3ecde4ae340bc79b4d55f38e82ab9d41",
     "_journal/2024-11-30.md": "c6040ba2caf1c9ff55faed25d7879e9a",
     "_journal/2024-11/2024-11-29.md": "4896d849b6345010669047323521e21a",
     "_journal/2024-11/2024-11-28.md": "dd843bc11263a1dca3c9e27ab4fd8c68",
@@ -1003,7 +1003,7 @@
     "_journal/2024-12/2024-12-04.md": "965f6619edf1002d960203e3e12a413b",
     "_journal/2024-12-06.md": "d75323d0fec57f4fc1f13cb4370df18d",
     "_journal/2024-12/2024-12-05.md": "4f3b1e7a43e01cc97b0eed6fbc6c1f96",
-    "calculus/integrals.md": "c5b5025d209a7a97a1b1c1e9345d7917",
+    "calculus/integrals.md": "1d34fb199b962f61cdc22f350817d5c3",
     "_journal/2024-12-07.md": "bfb6c4db0acbacba19f03a04ec29fa5c",
     "_journal/2024-12/2024-12-06.md": "d73b611d2d15827186a0252d9b9a6580",
     "_journal/2024-12-08.md": "5662897539b222db1af45dcd217f0796",
@@ -1029,7 +1029,7 @@
     "linkers/object-files.md": "77767f310330b8650a5023dd0522226c",
     "_journal/2024-12-16.md": "d867a62a955f3d080ae25f31464d53c4",
     "_journal/2024-12/2024-12-15.md": "be66c8808d8bb66d4e7b91db7c93c94a",
-    "linkers/elf.md": "6b54c2628bcd6e39df9cf3d09a68b62b",
+    "linkers/elf.md": "0734c90bf5b09319ae1f3bdd965de1c1",
     "c17/strings/printf.md": "8b67cfbccaf35dd9488b73e7e5555405",
     "c17/strings/index.md": "3fa6f42967f3cc786740bb8537c62682",
     "_journal/2024-12-17.md": "ae55db66c9835876c4a0343ac0806951",
@@ -1047,7 +1047,7 @@
     "encoding/xml/index.md": "01a66b1a102cccc682f8f1cab0f50bc6",
     "ontology/reification.md": "ef8275957dcc1a7e5501722d4652e41c",
     "ontology/rdf.md": "fd273c30bec6f46b68547f0d392620b1",
-    "data-models/rdf.md": "bf9c493ccbb5c47a6ad1b2e7820a0c77",
+    "data-models/rdf.md": "98594898837f981dcbdd26df80e93a87",
     "serialization/xml.md": "84b632282ebcc2b6216923a02abdd4c2",
     "serialization/index.md": "5ed7e99e4efc4844839ea357d351f5d8",
     "data-models/index.md": "9e60f40798490f0743f291e55f492033",
@@ -1055,7 +1055,7 @@
     "_journal/2024-12/2024-12-21.md": "1c1a5791f7519c92e882957cf417b51f",
     "formal-system/language.md": "7797d33a0b0eb187d43dda46a138fb25",
     "computability/automaton.md": "eb784de967ba7f26e99582d940a953fe",
-    "computability/index.md": "61a1bcd17133fe0fbb5e9c4fbb15597b",
+    "computability/index.md": "d7938428ed0b0224c1fe1e59d1fab118",
     "_journal/2024-12-23.md": "72b0964a8a5ed8ba0acf7fe10b5de279",
     "_journal/2024-12/2024-12-22.md": "75375a867efc5b3aff406c73394d4814",
     "computability/language.md": "9ee8bd16c231e71855ab1d8dae3188cb",
@@ -1072,8 +1072,12 @@
     "_journal/2024-12-27.md": "abc4a39a50305f3558181189eefb2058",
     "_journal/2024-12/2024-12-26.md": "59e59cad1ae568adbe8e27e98d36c59c",
     "combinators/index.md": "37ba794ba9a5ab84eb7452ed0a31aeec",
-    "_journal/2024-12-28.md": "7692126f76a32b785744adcbc76a58cb",
+    "_journal/2024-12-28.md": "1ad3caec4ea6f597cc5156f19b274c50",
-    "_journal/2024-12/2024-12-27.md": "abc4a39a50305f3558181189eefb2058"
+    "_journal/2024-12/2024-12-27.md": "abc4a39a50305f3558181189eefb2058",
+    "_journal/2024-12-29.md": "e7808872f56a12b51165fc86a1c48e60",
+    "_journal/2024-12/2024-12-28.md": "1ad3caec4ea6f597cc5156f19b274c50",
+    "data-models/rdf/sparql.md": "579cede269025cde2314c3052f272367",
+    "data-models/rdf/index.md": "979fa61c449648774438c4f29f782602"
   },
   "fields_dict": {
     "Basic": [

notes/_journal/2024-12-30.md

@@ -0,0 +1,9 @@
+---
+title: "2024-12-30"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)

notes/_journal/2024-12/2024-12-29.md

@@ -0,0 +1,12 @@
+---
+title: "2024-12-29"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)
+
+* Nore notes on cardinal number ordering.
+* Preliminary notes on [[rdf#SPARQL|SPARQL]].

notes/c17/alignment.md

@@ -516,7 +516,7 @@ END%%
 
 %%ANKI
 Basic
-What is the sign of the following bit-field?
+What is the signedness of the following bit-field?
 ```c
 struct foo { int bar : 1; };
 ```
@@ -527,7 +527,7 @@ END%%
 
 %%ANKI
 Basic
-What is the sign of the following bit-field?
+What is the signedness of the following bit-field?
 ```c
 struct foo { signed bar : 1; };
 ```
@@ -538,7 +538,7 @@ END%%
 
 %%ANKI
 Basic
-What is the sign of the following bit-field?
+What is the signedness of the following bit-field?
 ```c
 struct foo { unsigned bar : 1; };
 ```

notes/c17/linkage.md

@@ -229,7 +229,7 @@ END%%
 
 %%ANKI
 Basic
-What is the linkage of a local variable without a storage specified?
+What is the linkage of a local variable without a storage specifier?
 Back: None.
 Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
 <!--ID: 1733010193297-->

notes/c17/storage.md

@@ -298,7 +298,7 @@ END%%
 %%ANKI
 Basic
 Which storage class specifier(s) can be used to declare an object with automatic storage duration?
-Back: `auto` and {`register`}.
+Back: `auto` and `register`.
 Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
 <!--ID: 1733064332819-->
 END%%

notes/calculus/integrals.md

@@ -159,7 +159,7 @@ END%%
 %%ANKI
 Basic
 Let $s$ be a step function over $[a, b]$. What does $\int_a^b s(x) \,dx$ evaluate to after swapping limits of integration?
-Back: As $-\int_b^a s(x) \,dx$.
+Back: $-\int_b^a s(x) \,dx$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734816555515-->
 END%%
@@ -202,7 +202,7 @@ Let $s$ and $t$ be step functions defined on $[a, b]$. Then $$\int_a^b s(x) + t(
 
 %%ANKI
 Basic
-Let $s$ and $t$ be step functions over $[a, b]$. What does the additive property state?
+Let $s$ and $t$ be step functions over $[a, b]$. What does the additive property of integrals state?
 Back: $\int_a^b s(x) + t(x) \,dx = \int_a^b s(x) \,dx + \int_a^b t(x) \,dx$
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463659-->
@@ -231,7 +231,7 @@ Let $s$ be a step function defined on $[a, b]$. Let $c \in \mathbb{R}$. Then $$\
 
 %%ANKI
 Basic
-Let $s$ be a step function over $[a, b]$. What does the homogeneous property state?
+Let $s$ be a step function over $[a, b]$. What does the homogeneous property of integrals state?
 Back: For all $c \in \mathbb{R}$, $\int_a^b c \cdot s(x) \,dx = c \int_a^b s(x) \,dx$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463679-->
@@ -252,7 +252,7 @@ Let $s$ and $t$ be step functions defined on $[a, b]$. Let $c_1, c_2 \in \mathbb
 
 %%ANKI
 Basic
-Let $s$ and $t$ be step functions over $[a, b]$ and $c_1, c_2 \in \mathbb{R}$. What does the linearity property state?
+Let $s$ and $t$ be step functions over $[a, b]$ and $c_1, c_2 \in \mathbb{R}$. What does the linearity property of integrals state?
 Back: $\int_a^b [c_1 s(x) + c_2 t(x)] \,dx = c_1 \int_a^b s(x) \,dx + c_2 \int_a^b t(x) \,dx$
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463699-->
@@ -276,7 +276,7 @@ END%%
 
 %%ANKI
 Cloze
-The {linearity} property is a combination of the {additive} and {homogenous} properties.
+The {linearity} property of integrals is a combination of the {additive} and {homogenous} properties.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734814463693-->
 END%%
@@ -287,8 +287,8 @@ Let $s$ and $t$ be step functions defined on $[a, b]$. Suppose $s(x) < t(x)$ for
 
 %%ANKI
 Basic
-Let $s$ and $t$ be step functions over $[a, b]$. What does the comparison theorem state?
+Let $s$ and $t$ be step functions over $[a, b]$. What does the comparison theorem of integrals state?
-Back: If $s(x) < t(x)$ for all $x \in [a, b]$, $\int_a^b s(x) \,dx < \int_a^b t(x) \,dx$.
+Back: If $s(x) < t(x)$ for all $x \in [a, b]$, then $\int_a^b s(x) \,dx < \int_a^b t(x) \,dx$.
 Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
 <!--ID: 1734815755275-->
 END%%

notes/computability/index.md

@@ -183,14 +183,6 @@ Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third ed
 <!--ID: 1734903366666-->
 END%%
 
-%%ANKI
-Basic
-How is the concatenation of strings $x$ and $y$ over some alphabet denoted?
-Back: $xy$
-Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
-<!--ID: 1734903366671-->
-END%%
-
 %%ANKI
 Basic
 Let $x$ be a string over some alphabet. What does $xx$ denote?
@@ -201,7 +193,7 @@ END%%
 
 %%ANKI
 Cloze
-Let $x$ be a string over some alphabet. Then {$xx$} $=$ {$x^2$}.
+Let $x$ be a string over some alphabet. Then {$xx$} is equivalently denoted as {$x^2$}.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366679-->
 END%%
@@ -249,7 +241,7 @@ END%%
 %%ANKI
 Basic
 What is a language?
-Back: A nonempty set of strings.
+Back: A set of strings.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
 <!--ID: 1734903366705-->
 END%%

notes/data-models/rdf.md

@@ -126,7 +126,7 @@ END%%
 %%ANKI
 Basic
 RDF identifiers use what encoding?
-Back: URIs.
+Back: IRIs.
 Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
 <!--ID: 1722191359882-->
 END%%
@@ -142,7 +142,7 @@ END%%
 %%ANKI
 Basic
 How does RDF define a named graph?
-Back: A graph with a name.
+Back: As a graph (a set of triples) with a name.
 Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
 <!--ID: 1734804443462-->
 END%%
@@ -170,21 +170,33 @@ Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web
 <!--ID: 1734804443468-->
 END%%
 
+The RDF data model was designed from the beginning with [[federation|data federation]] in mind. Because every RDF store represents RDF data in the same way (i.e. as a set of triples), federation is as simple as combining the commonly encoded data into a single store before querying.
+
 %%ANKI
-Cloze
+Basic
-RDF is a {data model} whereas XML is a {serialization}.
+What mechanism makes RDF data federation easy?
+Back: Every source communicates data in the same way (i.e. as a set of triples).
 Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
-Tags: serialization::xml
+Tags: data_model::federation
-<!--ID: 1734805690321-->
+<!--ID: 1735176997772-->
 END%%
 
 %%ANKI
 Basic
-How might RDF and XML relate to one another?
+In the context of RDF, what does federation refer to?
-Back: XML can be used to serialize RDF.
+Back: The combining of multiple RDF stores into a single (possibly virtual) view.
 Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
-Tags: serialization::xml
+Tags: data_model::federation
-<!--ID: 1734805690328-->
+<!--ID: 1735176997776-->
+END%%
+
+%%ANKI
+Basic
+What does the federated graph refer to?
+Back: The graph produced by combining various federated data sources.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+Tags: data_model::federation
+<!--ID: 1735176997779-->
 END%%
 
 ## Blank Nodes
@@ -239,37 +251,203 @@ Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web
 <!--ID: 1735162429102-->
 END%%
 
-## Federation
+## Serializations
 
-The RDF data model was designed from the beginning with [[federation|data federation]] in mind. Because every RDF store represents RDF data in the same way (i.e. as a set of triples), federation is as simple as combining the commonly encoded data into a single store before querying.
+The original syntax and standard for writing RDF was RDF/XML. Turtle is an alternative, more human-readable, syntax. Besides these two exist many others.
 
 %%ANKI
 Basic
-What mechanism makes RDF data federation easy?
+Which RDF serialization is most widely used?
-Back: Every source communicates data in the same way (i.e. as a set of triples).
+Back: Turtle.
-Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+Reference: “Resource Description Framework,” in _Wikipedia_, November 25, 2024, [https://en.wikipedia.org/w/index.php?title=Resource_Description_Framework](https://en.wikipedia.org/w/index.php?title=Resource_Description_Framework&oldid=1259544587).
-Tags: data_model::federation
+<!--ID: 1735507470222-->
-<!--ID: 1735176997772-->
 END%%
 
 %%ANKI
 Basic
-In the context of RDF, what does federation refer to?
+Why is Turtle named the way it is?
-Back: The combining of multiple RDF stores into a single (possibly virtual) view.
+Back: It is an "acronym" for **Te**rse **R**DF **T**riple **L**anguag**e**.
-Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+Reference: “Resource Description Framework,” in _Wikipedia_, November 25, 2024, [https://en.wikipedia.org/w/index.php?title=Resource_Description_Framework](https://en.wikipedia.org/w/index.php?title=Resource_Description_Framework&oldid=1259544587).
-Tags: data_model::federation
+<!--ID: 1735507470227-->
-<!--ID: 1735176997776-->
 END%%
 
 %%ANKI
 Basic
-What does the federated graph refer to?
+What is RDF/XML a container for?
-Back: The graph produced by combining various federated data sources.
+Back: RDF data.
 Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
-Tags: data_model::federation
+<!--ID: 1735507470230-->
-<!--ID: 1735176997779-->
+END%%
+
+%%ANKI
+Basic
+What is Turtle a container for?
+Back: RDF data.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470233-->
+END%%
+
+%%ANKI
+Cloze
+RDF is a {data model} whereas XML is a {serialization format}.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+Tags: serialization::xml
+<!--ID: 1734805690321-->
+END%%
+
+%%ANKI
+Cloze
+RDF is a {data model} whereas Turtle is a {serialization format}.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470236-->
+END%%
+
+%%ANKI
+Basic
+How might RDF and XML relate to one another?
+Back: XML can be used to serialize RDF.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+Tags: serialization::xml
+<!--ID: 1734805690328-->
+END%%
+
+## SPARQL
+
+SPARQL (SPARQL Protocol and RDF Query Language) is the standard way to access RDF data using a query language. Query patterns are represented in a variant of Turtle, the most ubiquitous language used to express RDF itself.
+
+A server for the SPARQL protocol is called a **SPARQL endpoint**. It accepts SPARQL queries and returns results, according to the details of the protocol.
+
+%%ANKI
+Basic
+SPARQL syntax most closely resembles which RDF serialization format?
+Back: Turtle.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470239-->
+END%%
+
+%%ANKI
+Basic
+What is the standard means of querying an RDF store?
+Back: SPARQL.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735506488320-->
+END%%
+
+%%ANKI
+Basic
+What is SPARQL an acronym for?
+Back: **S**PARQL **P**rotocol **a**nd **R**DF **Q**uery **L**anguage.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735506488325-->
+END%%
+
+%%ANKI
+Cloze
+{1:SPARQL} is to {2:RDF} as {2:SQL} is to {1:RDBMS}.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735506488332-->
+END%%
+
+%%ANKI
+Basic
+The following snippet is an example of what language?
+```sparql
+SELECT ?movie WHERE {:JamesDean :playedIn ?movie}
+```
+Back: SPARQL
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735506488335-->
+END%%
+
+%%ANKI
+Basic
+What do the `:`s indicate in the following query?
+```sparql
+SELECT ?movie WHERE {:JamesDean :playedIn ?movie}
+```
+Back: The default namespace.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735506488338-->
+END%%
+
+%%ANKI
+Basic
+How are namespaces introduced in a SPARQL query?
+Back: With the `:` character.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470242-->
+END%%
+
+%%ANKI
+Basic
+What do the `?`s indicate in the following query?
+```sparql
+SELECT ?movie WHERE {:JamesDean :playedIn ?movie}
+```
+Back: Variables to be matched against.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735506488341-->
+END%%
+
+%%ANKI
+Basic
+How are variables introduced in a SPARQL query?
+Back: With the `?` character.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470245-->
+END%%
+
+%%ANKI
+Basic
+What do the curly braces (`{}`) indicate in the following query?
+```sparql
+SELECT ?movie WHERE {:JamesDean :playedIn ?movie}
+```
+Back: A graph pattern.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735506488344-->
+END%%
+
+%%ANKI
+Basic
+How are graph patterns introduced in a SPARQL query?
+Back: With the `{` and `}` characters.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470248-->
+END%%
+
+%%ANKI
+Basic
+In SPARQL, what is a graph pattern?
+Back: A graph with wildcards, used to match against a data graph.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735521898594-->
+END%%
+
+%%ANKI
+Cloze
+A {server for the SPARQL protocol} is called a {SPARQL endpoint}.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470252-->
+END%%
+
+%%ANKI
+Basic
+What is a SPARQL endpoint?
+Back: A server that can respond to SPARQL queries.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470256-->
+END%%
+
+%%ANKI
+Basic
+What does Allemang et al. describe as the most web-friendly way to provide access to RDF data?
+Back: Exposing a SPARQL endpoint to the data.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1735507470259-->
 END%%
 
 ## Bibliography
 
-* Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+* Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+* “Resource Description Framework,” in _Wikipedia_, November 25, 2024, [https://en.wikipedia.org/w/index.php?title=Resource_Description_Framework](https://en.wikipedia.org/w/index.php?title=Resource_Description_Framework&oldid=1259544587).

notes/linkers/elf.md

@@ -198,7 +198,7 @@ Thread-local global and static C variables initialized to a non-zero value.
 
 %%ANKI
 Basic
-What kind of global/static C variables does the `.tdata` section contain?
+What kind of global and static C variables does the `.tdata` section contain?
 Back: Thread-local variables initialized to a non-zero value.
 Reference: Ulrich Drepper, “ELF Handling For Thread-Local Storage,” n.d.
 Tags: c17
@@ -395,7 +395,7 @@ Uninitialized global and static thread-local C variables, along with any global
 
 %%ANKI
 Basic
-What kind of global/static C variables does the `.tbss` section contain?
+What kind of global and static C variables does the `.tbss` section contain?
 Back: Unitialized thread-local variables or those initialized to zero.
 Reference: Ulrich Drepper, “ELF Handling For Thread-Local Storage,” n.d.
 Tags: c17
@@ -422,8 +422,8 @@ END%%
 
 %%ANKI
 Basic
-Which two ELF sections contain global/static thread-local C variables?
+Which two ELF sections contain global and static thread-local C variables?
-Back: `.tdata` and `.bss`
+Back: `.tdata` and `.tbss`
 Reference: Ulrich Drepper, “ELF Handling For Thread-Local Storage,” n.d.
 Tags: c17
 <!--ID: 1734745402975-->
@@ -471,15 +471,6 @@ Tags: c17
 <!--ID: 1734745402993-->
 END%%
 
-%%ANKI
-Basic
-How does the size of the `.tbss` section compare to that of the `.tdata` section?
-Back: Less than or equal since the `.tbss` section is always empty.
-Reference: Ulrich Drepper, “ELF Handling For Thread-Local Storage,” n.d.
-Tags: c17
-<!--ID: 1734745402997-->
-END%%
-
 %%ANKI
 Basic
 Consider the following translation unit. Which ELF section will `bar` end up in?

notes/set/cardinality.md

@@ -1238,7 +1238,9 @@ END%%
 
 ### Ordering
 
-A set $A$ is **dominated** by a set $B$, written $A \preceq B$, if and only if there is a one-to-one function from $A$ into $B$. In other words, $A \preceq B$ if and only if $A$ is equinumerous to some subset of $B$.
+A set $A$ is **dominated** by a set $B$, written $A \preceq B$, if and only if there is a one-to-one function from $A$ into $B$. In other words, $A \preceq B$ if and only if $A$ is equinumerous to some subset of $B$. Then $$\mathop{\text{card}}A \leq \mathop{\text{card}}B \text{ if and only if } A \preceq B.$$
+
+Furthermore, $$\mathop{\text{card}}A < \mathop{\text{card}}B \text{ if and only if } A \preceq B \text{ and } A \not\approx B.$$
 
 %%ANKI
 Basic
@@ -1248,6 +1250,14 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1735353438914-->
 END%%
 
+%%ANKI
+Basic
+How do we denote that set $A$ is strictly dominated by set $B$?
+Back: $A \prec B$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305902-->
+END%%
+
 %%ANKI
 Basic
 Suppose $A \preceq B$. Then what must exist by definition?
@@ -1256,14 +1266,46 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1735353438921-->
 END%%
 
+%%ANKI
+Basic
+Suppose $A \prec B$. Then what must exist by definition?
+Back: A one-to-one function from $A$ into $B$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305907-->
+END%%
+
 %%ANKI
 Basic
 Suppose $A \preceq B$. Then what must $A$ be equinumerous to?
-Back: Some subset of $B$.
+Back: A subset of $B$.
 Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
 <!--ID: 1735353438924-->
 END%%
 
+%%ANKI
+Basic
+Suppose $A \preceq B$. Then what must $A$ *not* be equinumerous to?
+Back: N/A. There is no restriction here.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305910-->
+END%%
+
+%%ANKI
+Basic
+Suppose $A \prec B$. Then what must $A$ be equinumerous to?
+Back: A subset of $B$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305914-->
+END%%
+
+%%ANKI
+Basic
+Suppose $A \prec B$. Then what must $A$ *not* be equinumerous to?
+Back: $B$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305917-->
+END%%
+
 %%ANKI
 Basic
 What does $A \preceq B$ denote?
@@ -1272,6 +1314,14 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1735353438928-->
 END%%
 
+%%ANKI
+Basic
+What does $A \prec B$ denote?
+Back: That $A$ is strictly dominated by $B$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305921-->
+END%%
+
 %%ANKI
 Basic
 How do we expand expression $A \preceq B$ using FOL?
@@ -1280,6 +1330,124 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1735353438932-->
 END%%
 
+%%ANKI
+Basic
+How do we expand expression $A \prec B$ using FOL?
+Back: $A \not\approx B \land \exists C, C \subseteq B \land A \approx C$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305924-->
+END%%
+
+%%ANKI
+Basic
+Let $\kappa$ and $\lambda$ be cardinal numbers. How is $\kappa \leq \lambda$ defined?
+Back: As $K \preceq L$ for sets satisfying $\mathop{\text{card}}K = \kappa$ and $\mathop{\text{card}} L = \lambda$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305927-->
+END%%
+
+%%ANKI
+Basic
+Let $\kappa$ and $\lambda$ be cardinal numbers. How is $\kappa < \lambda$ defined?
+Back: As $K \preceq L$ and $K \not\approx L$ for sets satisfying $\mathop{\text{card}}K = \kappa$ and $\mathop{\text{card}} L = \lambda$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305931-->
+END%%
+
+%%ANKI
+Cloze
+{$\leq$} on cardinal numbers corresponds to {$\preceq$} on sets.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305934-->
+END%%
+
+%%ANKI
+Cloze
+{$<$} on cardinal numbers corresponds to {$\prec$} on sets.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305942-->
+END%%
+
+%%ANKI
+Basic
+How is $\mathop{\text{card} }K \leq \mathop{\text{card} }L$ defined in terms of equinumerosity?
+Back: $\mathop{\text{card} }K \leq \mathop{\text{card} }L$ iff $K$ is equinumerous to a subset of $L$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305947-->
+END%%
+
+%%ANKI
+Basic
+How is $\mathop{\text{card} }K < \mathop{\text{card} }L$ defined in terms of equinumerosity?
+Back: $\mathop{\text{card} }K < \mathop{\text{card} }L$ iff $K$ is equinumerous to a subset of $L$ and $K \not\approx L$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305952-->
+END%%
+
+%%ANKI
+Basic
+Let $\kappa$ and $\lambda$ be cardinal numbers. Restate the following in terms of sets: $$\kappa < \lambda \text{ iff } \kappa \leq \lambda \text{ and } \kappa \neq \lambda$$
+Back: Given $\mathop{\text{card}}K = \kappa$ and $\mathop{\text{card}}L = \lambda$, $\mathop{\text{card}}K < \mathop{\text{card}}L$ iff $K \preceq L$ and $K \not\approx L$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305957-->
+END%%
+
+%%ANKI
+Basic
+Let $K$ and $L$ be sets. Restate the following in terms of cardinal numbers: $$\mathop{\text{card}}K < \mathop{\text{card}}L \text{ iff } K \preceq L \text{ and } K \not\approx L.$$
+Back: Given $\mathop{\text{card}}K = \kappa$ and $\mathop{\text{card}}L = \lambda$,  $\kappa < \lambda$ iff $\kappa \leq \lambda$ and $\kappa \neq \lambda$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493305962-->
+END%%
+
+%%ANKI
+Basic
+Let $K$ and $L$ be sets. *Why* can't we use the following definition? $$\mathop{\text{card}} K \leq \mathop{\text{card}} L \text{ iff } \exists A \subseteq L, K \approx A$$
+Back: N/A. This is a suitable definition.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493767848-->
+END%%
+
+%%ANKI
+Basic
+Let $K$ and $L$ be sets. *Why* can't we use the following definition? $$\mathop{\text{card}} K < \mathop{\text{card}} L \text{ iff } \exists A \subset L, K \approx A$$
+Back: Infinite sets may be equinumerous to a proper subset of themselves.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735493767854-->
+END%%
+
+%%ANKI
+Basic
+For any $n \in \omega$, *why* is $n < \aleph_0$?
+Back: $n \not\approx \omega$ and there exists an injective function $f \colon n \rightarrow \omega$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735522988804-->
+END%%
+
+%%ANKI
+Basic
+For any cardinal number $\kappa$, *why* is $\kappa < 2^\kappa$?
+Back: Assuming $\mathop{\text{card}}K = \kappa$, $K \not\approx \mathscr{P}(K)$ and there exists an injective function $f \colon K \rightarrow \mathscr{P}(K)$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735522988810-->
+END%%
+
+%%ANKI
+Basic
+What is the smallest cardinal number?
+Back: $0$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735522988813-->
+END%%
+
+%%ANKI
+Basic
+What is the largest cardinal number?
+Back: N/A. There is no largest cardinal number.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1735522988817-->
+END%%
+
 ## Bibliography
 
 * Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).