From cfa95d2390b0dcc6a1ffee10d1cb675d8e1967ce Mon Sep 17 00:00:00 2001 From: Joshua Potter Date: Thu, 6 Jun 2024 07:14:13 -0600 Subject: [PATCH] Notes on ordered pairs. --- .../plugins/obsidian-to-anki-plugin/data.json | 24 ++- notes/_journal/2024-06-06.md | 11 ++ notes/_journal/{ => 2024-06}/2024-06-03.md | 0 notes/_journal/2024-06/2024-06-04.md | 12 ++ notes/_journal/2024-06/2024-06-05.md | 11 ++ notes/algebra/boolean.md | 37 ++++- notes/algebra/set.md | 28 ++++ notes/programming/lambda-calculus.md | 86 ++++++++++ notes/set/index.md | 13 +- notes/set/relations.md | 149 ++++++++++++++++++ notes/x86-64/instructions.md | 8 - 11 files changed, 359 insertions(+), 20 deletions(-) create mode 100644 notes/_journal/2024-06-06.md rename notes/_journal/{ => 2024-06}/2024-06-03.md (100%) create mode 100644 notes/_journal/2024-06/2024-06-04.md create mode 100644 notes/_journal/2024-06/2024-06-05.md create mode 100644 notes/set/relations.md diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index 3d0fd6d..c585a60 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -133,7 +133,8 @@ "venn-diagram-union.png", "venn-diagram-intersection.png", "venn-diagram-rel-comp.png", - "venn-diagram-abs-comp.png" + "venn-diagram-abs-comp.png", + "venn-diagram-symm-diff.png" ], "File Hashes": { "algorithms/index.md": "3ac071354e55242919cc574eb43de6f8", @@ -313,7 +314,7 @@ "_journal/2024-03-18.md": "8479f07f63136a4e16c9cd07dbf2f27f", "_journal/2024-03/2024-03-17.md": "23f9672f5c93a6de52099b1b86834e8b", "set/directed-graph.md": "b4b8ad1be634a0a808af125fe8577a53", - "set/index.md": "55a80d53973af2c0343438346e2086b2", + "set/index.md": "d1fcdfe4506aab4ec86f30118464fb2a", "set/graphs.md": "4bbcea8f5711b1ae26ed0026a4a69800", "_journal/2024-03-19.md": "a0807691819725bf44c0262405e97cbb", "_journal/2024-03/2024-03-18.md": "63c3c843fc6cfc2cd289ac8b7b108391", @@ -332,7 +333,7 @@ "_journal/2024-03-22.md": "8da8cda07d3de74f7130981a05dce254", "_journal/2024-03/2024-03-21.md": "cd465f71800b080afa5c6bdc75bf9cd3", "x86-64/declarations.md": "75bc7857cf2207a40cd7f0ee056af2f2", - "x86-64/instructions.md": "c9ae5dedaa22fbcdc486663877fc1c1e", + "x86-64/instructions.md": "06b7fbe1a7a9568b80239310eb72e87a", "git/refs.md": "e20c2c9b14ba6c2bd235416017c5c474", "set/trees.md": "b085bd8d08dccd8cbf02bb1b7a4baa43", "_journal/2024-03-24.md": "1974cdb9fc42c3a8bebb8ac76d4b1fd6", @@ -466,7 +467,7 @@ "programming/λ-Calculus.md": "bf36bdaf85abffd171bb2087fb8228b2", "_journal/2024-05-23.md": "9d9106a68197adcee42cd19c69d2f840", "_journal/2024-05/2024-05-22.md": "3c29eec25f640183b0be365e7a023750", - "programming/lambda-calculus.md": "547bc98111e516fc70a415d91db7b3ff", + "programming/lambda-calculus.md": "89f024561ea770552bc20056a45dbce6", "_journal/2024-05-25.md": "04e8e1cf4bfdbfb286effed40b09c900", "_journal/2024-05/2024-05-24.md": "86132f18c7a27ebc7a3e4a07f4867858", "_journal/2024-05/2024-05-23.md": "d0c98b484b1def3a9fd7262dcf2050ad", @@ -474,8 +475,8 @@ "_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": "049c5ff36ce8fe99b2c8a8f452d0514f", - "algebra/boolean.md": "56d2e0be2853d49b5dface7fa2d785a9", + "algebra/set.md": "92de8c0197cef54b5c6c269aac6b93b2", + "algebra/boolean.md": "ee41e624f4d3d3aca00020d9a9ae42c8", "git/merge-conflicts.md": "af3603c7a8fde60a1982c0950d209b77", "_journal/2024-05-28.md": "0f6aeb5ec126560acdc2d8c5c6570337", "_journal/2024-05/2024-05-27.md": "e498d5154558ebcf7261302403ea8016", @@ -489,10 +490,17 @@ "_journal/2024-05/2024-05-31.md": "4421312bffa6f3c7e501a28be1e3bd5b", "_journal/2024-06-02.md": "0059e0332794e0007545b92bc4c1ff9f", "_journal/2024-06/2024-06-01.md": "6d39286db9d89975e441c57f6a92cfaf", - "_journal/2024-06-03.md": "560019592d88237bdb4b0ea609465ef6", + "_journal/2024-06-03.md": "3dbe96317f721515f3e6a20b82e3d537", "_journal/2024-06/2024-06-02.md": "0059e0332794e0007545b92bc4c1ff9f", "programming/lean.md": "2815eac192c7e231937e2369817a6dc1", - "logic/equality.md": "1867b676e0e7c9ec8f1addc40fefb966" + "logic/equality.md": "1867b676e0e7c9ec8f1addc40fefb966", + "_journal/2024-06-04.md": "a7ca58741dbfdd7e351d835db3884c68", + "_journal/2024-06/2024-06-03.md": "3dbe96317f721515f3e6a20b82e3d537", + "_journal/2024-06-05.md": "60f82c089f6911db8541a0bca7505ab4", + "_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": "411e81682aa5a731cd501031dc3ab59d" }, "fields_dict": { "Basic": [ diff --git a/notes/_journal/2024-06-06.md b/notes/_journal/2024-06-06.md new file mode 100644 index 0000000..ec90de7 --- /dev/null +++ b/notes/_journal/2024-06-06.md @@ -0,0 +1,11 @@ +--- +title: "2024-06-06" +--- + +- [x] Anki Flashcards +- [x] KoL +- [x] OGS +- [ ] Sheet Music (10 min.) +- [ ] Korean (Read 1 Story) + +* Notes on [[relations#Overview|ordered pairs]]. \ No newline at end of file diff --git a/notes/_journal/2024-06-03.md b/notes/_journal/2024-06/2024-06-03.md similarity index 100% rename from notes/_journal/2024-06-03.md rename to notes/_journal/2024-06/2024-06-03.md diff --git a/notes/_journal/2024-06/2024-06-04.md b/notes/_journal/2024-06/2024-06-04.md new file mode 100644 index 0000000..0e3e447 --- /dev/null +++ b/notes/_journal/2024-06/2024-06-04.md @@ -0,0 +1,12 @@ +--- +title: "2024-06-04" +--- + +- [x] Anki Flashcards +- [x] KoL +- [x] OGS +- [ ] Sheet Music (10 min.) +- [ ] Korean (Read 1 Story) + +* Notes on [[set#Symmetric Difference|symmetric differences]] of sets. +* Finished Chapter 2 exercises in "Elements of Set Theory". \ No newline at end of file diff --git a/notes/_journal/2024-06/2024-06-05.md b/notes/_journal/2024-06/2024-06-05.md new file mode 100644 index 0000000..87fbb64 --- /dev/null +++ b/notes/_journal/2024-06/2024-06-05.md @@ -0,0 +1,11 @@ +--- +title: "2024-06-05" +--- + +- [x] Anki Flashcards +- [x] KoL +- [x] OGS +- [ ] Sheet Music (10 min.) +- [ ] Korean (Read 1 Story) + +* Read chapter 18.10.2 and 15.4 in "Database System Concepts". \ No newline at end of file diff --git a/notes/algebra/boolean.md b/notes/algebra/boolean.md index 6638b63..cf56741 100644 --- a/notes/algebra/boolean.md +++ b/notes/algebra/boolean.md @@ -180,22 +180,55 @@ END%% %%ANKI Basic -What C bit-level operator corresponds to $\cup$? +What C bit-level operator corresponds to set notation $\cup$? Back: `|` Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: binary c17 set END%% +%%ANKI +Cloze +{$\cup$} is to the algebra of sets whereas {$\lor$} is to boolean algebra. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). +Tags: set + +END%% + %%ANKI Basic -What C bit-level operator corresponds to $\cap$? +What C bit-level operator corresponds to set notation $\cap$? Back: `&` Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: binary c17 set END%% +%%ANKI +Cloze +{$\cap$} is to the algebra of sets whereas {$\land$} is to boolean algebra. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). +Tags: set + +END%% + +%%ANKI +Basic +What C bit-level operator corresponds to set notation $\triangle$? +Back: `^` +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. +Tags: binary c17 set + +END%% + +%%ANKI +Cloze +{$\triangle$} is to the algebra of sets whereas {$\oplus$} is to boolean algebra. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). +Tags: set + +END%% + %%ANKI Basic What is a bit mask? diff --git a/notes/algebra/set.md b/notes/algebra/set.md index d93da8f..e9c8fe6 100644 --- a/notes/algebra/set.md +++ b/notes/algebra/set.md @@ -520,6 +520,34 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre END%% +## Symmetric Difference + +Define the **symmetric difference** of sets $A$ and $B$ as $$A \mathop{\triangle} B = (A - B) \cup (B - A)$$ + +%%ANKI +Basic +What two operators are used in the definition of the symmetric difference? +Back: $\cup$ and $-$. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +How is the symmetric difference of sets $A$ and $B$ denoted? +Back: $A \mathop{\triangle} B$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +How is $A \mathop{\triangle} B$ defined? +Back: As $(A - B) \cup (B - A)$. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + ## Bibliography * Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). \ No newline at end of file diff --git a/notes/programming/lambda-calculus.md b/notes/programming/lambda-calculus.md index 9b2fb6e..31f8565 100644 --- a/notes/programming/lambda-calculus.md +++ b/notes/programming/lambda-calculus.md @@ -16,6 +16,14 @@ Assume that there is given an infinite sequence of expressions called **variable If the sequence of atomic constants is empty, the system is called **pure**. Otherwise it is called **applied**. +%%ANKI +Basic +Who is usually attributed the creation of $\lambda$-calculus? +Back: Alonzo Church. +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + %%ANKI Basic What does a "higher-order function" refer to? @@ -769,6 +777,84 @@ Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combi END%% +For all $\lambda$-terms $M$, $N$, and variables $x$: + +* $[x/x]M \equiv M$ +* $x \not\in FV(M) \Rightarrow [N/x]M \equiv M$ +* $x \in FV(M) \Rightarrow FV([N/x]M) = FV(N) \cup (FV(M) - \{x\})$ + +%%ANKI +Basic +What is the result of $[x/x]M$? +Back: $M$. +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +If $x \not\in FV(M)$, what is the result of $[N/x]M$? +Back: $M$ +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +Suppose $x \in FV(M)$. How is $FV([N/x]M)$ equivalently written without substitution? +Back: $FV(N) \cup (FV(M) - \{x\})$ +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +Suppose $x \in FV(M)$. How is $FV(N) \cup (FV(M) - \{x\})$ more simply written using substitution? +Back: $FV([N/x]M)$ +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +What is the result of $lgh([y/x]M)$? +Back: $lgh(M)$ +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +$[N/x]M$ corresponds to which equivalence-transformation inference rule? +Back: Substitution. +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +$[P/v][v/x]M \equiv [P/x]M$ corresponds to which equivalence-transformation inference rule? +Back: Transitivity. +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +Rewrite $(E_u^x)_v^x$ using $\lambda$-calculus syntax. +Back: $[v/x][u/x]E$ +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + +%%ANKI +Basic +Rewrite $[x/v][v/x]M$ using equivalence-transformation syntax. +Back: $(M^x_v)^v_x$ +Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). + +END%% + ## Bibliography * Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf). \ No newline at end of file diff --git a/notes/set/index.md b/notes/set/index.md index a149916..fb25007 100644 --- a/notes/set/index.md +++ b/notes/set/index.md @@ -468,7 +468,7 @@ END%% %%ANKI Basic -What advantage does the general form of the union axiom have over its prelimiary form? +What advantage does the general form of the union axiom have over its preliminary form? Back: The general form can handle infinite sets. Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). @@ -746,7 +746,7 @@ END%% %%ANKI Basic -What is the result of $\bigcap \{\{2, 4, 6\}, \{6, 16, 26\}, \{0\}\}$? +What is the result of $\bigcap \{\{2, 4, 6\}, \{6, 16, 26\}, \{6\}\}$? Back: $\{6\}$ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). @@ -809,6 +809,15 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre END%% +%%ANKI +Basic +What set operation is shaded green in the following venn diagram? +![[venn-diagram-symm-diff.png]] +Back: $A \mathop{\triangle} B$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + %%ANKI Basic The "subset axioms" are more accurately classified as what? diff --git a/notes/set/relations.md b/notes/set/relations.md new file mode 100644 index 0000000..03feaab --- /dev/null +++ b/notes/set/relations.md @@ -0,0 +1,149 @@ +--- +title: Relations +TARGET DECK: Obsidian::STEM +FILE TAGS: set::relation +tags: + - relation + - set +--- + +## Overview + +An ordered pair of $x$ and $y$, denoted $\langle x, y \rangle$, is defined as: $\langle x, y \rangle = \{\{x\}, \{x, y\}\}$. We define the **first coordinate** of $\langle x, y \rangle$ to be $x$ and the **second coordinate** to be $y$. + +%%ANKI +Basic +How is an ordered pair of $x$ and $y$ denoted? +Back: $\langle x, y \rangle$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +What property must any satisfactory definition of $\langle x, y \rangle$ satisfy? +Back: $x$ and $y$, along with their order, are uniquely determined. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Which of ordered pairs or sets is more general? +Back: Sets. + +END%% + +%%ANKI +Basic +What biconditional is used to prove the well-definedness of $\langle x, y \rangle$? +Back: $(\langle x, y \rangle = \langle u, v \rangle) \Leftrightarrow (x = u \land y = v)$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Cloze +{$\{1, 2\}$} is a set whereas {$\langle 1, 2 \rangle$} is an ordered pair. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +How is $\langle x, y \rangle$ usually defined? +Back: As $\{\{x\}, \{x, y\}\}$. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Who is usually attributed the most commonly used definition of an ordered pair? +Back: Kazimierz Kuratowski. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +How is $\{\{x\}, \{x, y\}\}$ alternatively denoted? +Back: $\langle x, y \rangle$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Cloze +Well-definedness of ordered pairs: {$\langle u, v \rangle = \langle x, y \rangle$} if and only if {$u = x \land v = y$}. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +What term is used to refer to $x$ in $\langle x, y \rangle$? +Back: The first coordinate. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Cloze +$y$ is the {second} coordinate of $\langle x, y \rangle$. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +Given two sets $A$ and $B$, the **Cartesian product** $A \times B$ is defined as: $$A \times B = \{\langle x, y \rangle \mid x \in A \land y \in B\}$$ + +%%ANKI +Basic +How is the Cartesian product of $A$ and $B$ denoted? +Back: $A \times B$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Using ordered pairs, how is $A \times B$ defined? +Back: $\{\langle x, y \rangle \mid x \in A \land y \in B\}$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Who is attributed the representation of points in a plane? +Back: René Descartes. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Why is the Cartesian product named the way it is? +Back: It is named after René Descartes. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Suppose $x, y \in A$. What set is $\langle x, y \rangle$ in? +Back: $\mathscr{P}\mathscr{P}A$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Cloze +{$x \in A$} iff {$\{x\} \subseteq A$} iff {$\{x\} \in \mathscr{P}A$}. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +## Bibliography + +* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). \ No newline at end of file diff --git a/notes/x86-64/instructions.md b/notes/x86-64/instructions.md index 62ca2c1..d41dc5b 100644 --- a/notes/x86-64/instructions.md +++ b/notes/x86-64/instructions.md @@ -82,14 +82,6 @@ There are three types of operands: | Memory | $(r_b,r_i,s)$ | $M[R[r_b] + R[r_i] \cdot s]$ | Scaled indexed | | Memory | $Imm(r_b,r_i,s)$ | $M[Imm + R[r_b] + R[r_i] \cdot s]$ | Scaled indexed | -%%ANKI -Basic -What are the three types of operands instructions can act on? -Back: Immediates, registers, and memory addresses. -Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. - -END%% - %%ANKI Basic What are the types of source operands instructions can specify?