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Archimedean property and natural numbers.

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Joshua Potter 2024-08-24 02:07:51 -06:00
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---
title: "2024-08-24"
---
- [ ] Anki Flashcards
- [ ] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Began notes on [[natural-numbers|natural numbers]].

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---
title: "2024-08-20"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Add flashcards on the [[arch-prop|Archimedean property]] of reals.

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---
title: "2024-08-21"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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---
title: "2024-08-22"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Watched [Lecture 11 - Join Algorithms](https://www.youtube.com/watch?v=yFk_GfaY2Hk&list=PLSE8ODhjZXjaKScG3l0nuOiDTTqpfnWFf).

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---
title: "2024-08-23"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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---
title: Archimedean Property
TARGET DECK: Obsidian::STEM
FILE TAGS: algebra::archimedean
tags:
- algebra
---
## Overview
If $x, y \in \mathbb{R}^+$, then there exists a positive integer $n$ such that $nx > y$. This fundamental property usually follows from the [[bounds#Completeness Axiom|completeness axiom]].
%%ANKI
Basic
What does the Archimedean property of the reals state?
Back: If $x, y \in \mathbb{R}^+$, then there exists a positive integer $n$ such that $nx > y$.
Reference: “Archimedean Property,” in _Wikipedia_, June 23, 2024, [https://en.wikipedia.org/w/index.php?title=Archimedean_property](https://en.wikipedia.org/w/index.php?title=Archimedean_property&oldid=1230567137).
<!--ID: 1724155425457-->
END%%
%%ANKI
Basic
How is the Archimedean property of the reals geometrically interpreted?
Back: Any finite-length line segment can be covered by a finite number of line segments of some positive length.
Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
<!--ID: 1724155425465-->
END%%
%%ANKI
Basic
The Archimedean property of the reals posits the existence of what mathematical entity?
Back: A positive integer.
Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
<!--ID: 1724155425470-->
END%%
%%ANKI
Basic
Given positive reals $x$ and $y$, what does the Archimedean property conclude?
Back: There exists a positive integer $n$ such that $nx > y$.
Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
<!--ID: 1724155425481-->
END%%
%%ANKI
Basic
Given reals $x$ and $y$, what does the Archimedean property conclude?
Back: Indeterminate. We expect $x$ and $y$ to be positive reals.
Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
<!--ID: 1724155425487-->
END%%
%%ANKI
Basic
Which property is roughly described as "the reals have no infinitely large element?"
Back: The Archimedean property of the reals.
Reference: “Archimedean Property,” in _Wikipedia_, June 23, 2024, [https://en.wikipedia.org/w/index.php?title=Archimedean_property](https://en.wikipedia.org/w/index.php?title=Archimedean_property&oldid=1230567137).
<!--ID: 1724155425492-->
END%%
%%ANKI
Basic
Which property of the reals is depicted in the following?
![[archimedean-property.png]]
Back: The Archimedean property.
Reference: “Archimedean Property,” in _Wikipedia_, June 23, 2024, [https://en.wikipedia.org/w/index.php?title=Archimedean_property](https://en.wikipedia.org/w/index.php?title=Archimedean_property&oldid=1230567137).
<!--ID: 1724155425498-->
END%%
%%ANKI
Basic
How is the following diagram stated analytically?
![[archimedean-property.png]]
Back: For any $A, B \in \mathbb{R}^+$, there exists a positive integer $n$ such that $nA > B$.
Reference: “Archimedean Property,” in _Wikipedia_, June 23, 2024, [https://en.wikipedia.org/w/index.php?title=Archimedean_property](https://en.wikipedia.org/w/index.php?title=Archimedean_property&oldid=1230567137).
<!--ID: 1724155425503-->
END%%
%%ANKI
Basic
What mathematical entities are assumed to exist in the formulate of the Archimedean property of the reals?
Back: Two positive real numbers.
Reference: “Archimedean Property,” in _Wikipedia_, June 23, 2024, [https://en.wikipedia.org/w/index.php?title=Archimedean_property](https://en.wikipedia.org/w/index.php?title=Archimedean_property&oldid=1230567137).
<!--ID: 1724155425509-->
END%%
%%ANKI
Basic
What axiom of the real-number system is used to prove its Archimedean property?
Back: The least upper bound axiom (i.e. the completeness axiom).
Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
<!--ID: 1724155536942-->
END%%
## Bibliography
* “Archimedean Property,” in _Wikipedia_, June 23, 2024, [https://en.wikipedia.org/w/index.php?title=Archimedean_property](https://en.wikipedia.org/w/index.php?title=Archimedean_property&oldid=1230567137).
* Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).

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@ -1081,14 +1081,6 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
<!--ID: 1720782833233-->
END%%
%%ANKI
Basic
For any function $F \colon A \rightarrow B$, $F$ is a member of what other set?
Back: $\mathscr{P}(A \times B)$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1720782833236-->
END%%
%%ANKI
Basic
For sets $A$ and $B$, how is set $B^A$ pronounced?

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@ -15,7 +15,7 @@ This quote describes C's **abstract state machine**. Whatever instructions a C p
%%ANKI
Basic
What feature of C's abstract state machine makes C performant?
Back: It enables optimization.
Back: The ability to optimize.
Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
<!--ID: 1723856661330-->
END%%

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@ -27,7 +27,7 @@ END%%
%%ANKI
Basic
Why are narrow types named the way they are?
Back: They are considered to small to be used directly in arithmetic expressions.
Back: They are considered too small to be used directly in arithmetic expressions.
Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
<!--ID: 1723859121959-->
END%%

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@ -979,7 +979,7 @@ END%%
%%ANKI
Basic
When are both of the following guarded commands executed? $$\begin{align*} \textbf{if } & x \geq 0 \rightarrow z \coloneqq x \\ \textbf{ | } & x \leq 0 \rightarrow z \coloneqq -x \\ \textbf{fi } & \end{align*}$$
Back: N/A.
Back: N/A. Only one guard is executed.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1722257348960-->
END%%

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@ -1115,6 +1115,33 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
<!--ID: 1720964209648-->
END%%
## Infinity Axiom
There exists an [[natural-numbers#Inductive Sets|inductive]] set: $$\exists A, [\varnothing \in A \land (\forall a \in A, a^+ \in A)]$$
%%ANKI
Basic
What does the infinity axiom state?
Back: There exists an inductive set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269578-->
END%%
%%ANKI
Cloze
The {infinity axiom} asserts the existence of an {inductive set}.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269581-->
END%%
%%ANKI
Basic
State the infinity axiom in FOL.
Back: $\exists A, [\varnothing \in A \land (\forall a \in A, a^+ \in A)]$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269585-->
END%%
## Bibliography
* “Axiom of Choice,” in _Wikipedia_, July 8, 2024, [https://en.wikipedia.org/w/index.php?title=Axiom_of_choice&oldid=1233242262](https://en.wikipedia.org/w/index.php?title=Axiom_of_choice&oldid=1233242262).

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---
title: Natural Numbers
TARGET DECK: Obsidian::STEM
FILE TAGS: set::nat
tags:
- natural-number
- set
---
## Overview
The standard way of representing the natural numbers is as follows:
* $0 = \varnothing$
* $1 = \{0\} = \{\varnothing\}$
* $2 = \{0, 1\} = \{\varnothing, \{\varnothing\}\}$
* $\ldots$
That is, each natural number corresponds to the set of natural numbers smaller than it.
%%ANKI
Basic
How is the number $0$ represented as a set?
Back: $\varnothing$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233219-->
END%%
%%ANKI
Basic
How is the number $1$ represented as a set?
Back: $\{0\} = \{\varnothing\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233247-->
END%%
%%ANKI
Basic
How is the number $2$ represented as a set?
Back: $\{0, 1\} = \{\varnothing, \{\varnothing\}\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233252-->
END%%
%%ANKI
Basic
Who came up with the standard set representation of natural numbers?
Back: John von Neumann.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233257-->
END%%
%%ANKI
Basic
Consider the set representation of $n \in \mathbb{N}$. How many members does $n$ have?
Back: $n$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233263-->
END%%
%%ANKI
Basic
Consider the set representation of $n \in \mathbb{N}$. What are the members of $n$?
Back: $0$, $1$, $\ldots$, $n - 1$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233269-->
END%%
%%ANKI
Basic
Let $n \in \mathbb{N}$. *Why* is $n \in n + 1$?
Back: $n + 1$ is a set containing all preceding natural numbers.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233274-->
END%%
%%ANKI
Basic
Let $n \in \mathbb{N}$. *Why* is $n \subseteq n + 1$?
Back: $n$ and $n + 1$ are sets containing all their preceding natural numbers.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233279-->
END%%
## Inductive Sets
For any set $a$, its **successor** $a^+$ is defined as $$a^+ = a \cup \{a\}$$
%%ANKI
Basic
How is the successor of a set $a$ denoted?
Back: $a^+$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233287-->
END%%
%%ANKI
Basic
How is the successor of a set $a$ defined?
Back: As $a^+ = a \cup \{a\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233291-->
END%%
%%ANKI
Basic
Set $\{a, b\}^+$ equals what other set?
Back: $\{a, b, \{a, b\}\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233295-->
END%%
%%ANKI
Basic
Set $\{a\}^+$ equals what other set?
Back: $\{a, \{a\}\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233299-->
END%%
%%ANKI
Basic
Set $\{a, \{a, b\}, \{a, b, c\}\}$ can be written as the successor of what set?
Back: N/A.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485516768-->
END%%
%%ANKI
Basic
Set $\{a, b, \{a, b\}\}$ can be written as the successor of what set?
Back: $\{a, b\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485516774-->
END%%
%%ANKI
Basic
Set $\{a, \{a, b\}\}$ can be written as the successor of what set?
Back: N/A.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485516777-->
END%%
%%ANKI
Basic
Set $\{a, \{a, b\}, \{a, \{a, b\}\}\}$ can be written as the successor of what set?
Back: $\{a, \{a, b\}\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485516780-->
END%%
%%ANKI
Basic
If $n \in \mathbb{N}$ then $n \in n + 1$. What analagous statement holds for arbitrary set $a$?
Back: $a \in a^+$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233303-->
END%%
%%ANKI
Basic
If $n \in \mathbb{N}$ then $n \subseteq n + 1$. What analagous statement holds for arbitrary set $a$?
Back: $a \subseteq a^+$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724485233283-->
END%%
A set $A$ is **inductive** if and only if $\varnothing \in A$ and $\forall a \in A, a^+ \in A$.
%%ANKI
Basic
What does it mean for a set $A$ to be closed under successor?
Back: If $a \in A$, then $a^+ \in A$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269548-->
END%%
%%ANKI
Basic
Write "set $B$ is closed under successor" in FOL.
Back: $\forall b \in B, b^+ \in B$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269552-->
END%%
%%ANKI
Basic
What does it mean for a set $A$ to be inductive?
Back: $\varnothing \in A$ and $A$ is closed under successor.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269555-->
END%%
%%ANKI
Cloze
A set $A$ is inductive iff {$\varnothing \in A$} and {$A$ is closed under successor}.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269558-->
END%%
%%ANKI
Basic
An inductive set is closed under what operation?
Back: Successor.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269562-->
END%%
%%ANKI
Basic
What set is the "seed" of an inductive set?
Back: $\varnothing$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269565-->
END%%
%%ANKI
Basic
Let $a \in A$ where $A$ is an inductive set. What other members must belong to $A$?
Back: $a^+$, $a^{++}$, $\ldots$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269568-->
END%%
%%ANKI
Basic
What natural number corresponds to $\varnothing^{+++}$?
Back: $3$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269571-->
END%%
%%ANKI
Basic
What natural number corresponds to $\varnothing$?
Back: $0$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486269575-->
END%%
A **natural number** is a set that belongs to every inductive set.
%%ANKI
Basic
How is a natural number *defined* in set theory?
Back: As a set belonging to every inductive set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486756997-->
END%%
%%ANKI
Basic
What greek letter is used to denote the set of natural numbers?
Back: $\omega$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486757001-->
END%%
%%ANKI
Basic
What is the smallest inductive set?
Back: $\omega$, i.e. the set of natural numbers.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486757004-->
END%%
%%ANKI
Basic
How might $\omega$ be defined as an intersection of classes?
Back: $\omega = \bigcap\,\{A \mid A \text{ is inductive}\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1724486757007-->
END%%
%%ANKI
Basic
Suppose $n \in \omega$. What other sets *must* $n$ be a member of?
Back: Every other inductive set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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END%%
## Bibliography
* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).

20
notes/set/order.md
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@ -89,7 +89,7 @@ END%%
%%ANKI
Cloze
Operator {$\leq$} typically denote a {non-strict} preorder.
Operator {$\leq$} typically denotes a {non-strict} preorder.
Reference: “Preorder,” in _Wikipedia_, July 21, 2024, [https://en.wikipedia.org/w/index.php?title=Preorder](https://en.wikipedia.org/w/index.php?title=Preorder&oldid=1235839474).
<!--ID: 1723924394146-->
END%%
@ -177,7 +177,7 @@ END%%
%%ANKI
Cloze
Operator {$<$} typically denote a {strict} preorder.
Operator {$<$} typically denotes a {strict} preorder.
Reference: “Preorder,” in _Wikipedia_, July 21, 2024, [https://en.wikipedia.org/w/index.php?title=Preorder](https://en.wikipedia.org/w/index.php?title=Preorder&oldid=1235839474).
<!--ID: 1723924394151-->
END%%
@ -268,7 +268,7 @@ END%%
%%ANKI
Basic
*Why* isn't $R = \{\langle a, a \rangle, \langle b, c \rangle\}$ a partial order on $\{a, b, c\}$?
Back: N/A. It is.
Back: It isn't reflexive on $\{b, c\}$.
Reference: “Partially Ordered Set,” in _Wikipedia_, June 22, 2024, [https://en.wikipedia.org/w/index.php?title=Partially_ordered_set](https://en.wikipedia.org/w/index.php?title=Partially_ordered_set&oldid=1230452839).
<!--ID: 1723816108524-->
END%%
@ -276,7 +276,7 @@ END%%
%%ANKI
Basic
*Why* isn't $R = \{\langle a, a \rangle, \langle b, c \rangle, \langle c, b \rangle\}$ a partial order on $\{a, b, c\}$?
Back: It isn't antisymmetric.
Back: It isn't reflexive on $\{b, c\}$, it isn't antisymmetric, and it isn't transitive.
Reference: “Partially Ordered Set,” in _Wikipedia_, June 22, 2024, [https://en.wikipedia.org/w/index.php?title=Partially_ordered_set](https://en.wikipedia.org/w/index.php?title=Partially_ordered_set&oldid=1230452839).
<!--ID: 1723816108531-->
END%%
@ -309,14 +309,14 @@ END%%
%%ANKI
Cloze
Operator {$<$} typically denote a {strict} partial order.
Operator {$<$} typically denotes a {strict} partial order.
Reference: “Partially Ordered Set,” in _Wikipedia_, June 22, 2024, [https://en.wikipedia.org/w/index.php?title=Partially_ordered_set](https://en.wikipedia.org/w/index.php?title=Partially_ordered_set&oldid=1230452839).
<!--ID: 1723902024378-->
END%%
%%ANKI
Cloze
Operator {$\leq$} typically denote a {non-strict} partial order.
Operator {$\leq$} typically denotes a {non-strict} partial order.
Reference: “Partially Ordered Set,” in _Wikipedia_, June 22, 2024, [https://en.wikipedia.org/w/index.php?title=Partially_ordered_set](https://en.wikipedia.org/w/index.php?title=Partially_ordered_set&oldid=1230452839).
<!--ID: 1723902024382-->
END%%
@ -414,7 +414,7 @@ END%%
%%ANKI
Basic
*Why* isn't $R = \{\langle a, a \rangle, \langle b, c \rangle\}$ an equivalence relation on $\{a, b\}$?
Back: It isn't symmetric.
Back: It is neither reflexive on $\{a, b\}$ nor symmetric.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1723816108538-->
END%%
@ -855,7 +855,7 @@ END%%
%%ANKI
Cloze
Operator {$\leq$} typically denote a {non-strict} total order.
Operator {$\leq$} typically denotes a {non-strict} total order.
Reference: “Total Order.” In _Wikipedia_, April 9, 2024. [https://en.wikipedia.org/w/index.php?title=Total_order](https://en.wikipedia.org/w/index.php?title=Total_order&oldid=1218090468).
<!--ID: 1723923665325-->
END%%
@ -896,7 +896,7 @@ END%%
%%ANKI
Cloze
Operator {$<$} typically denote a {strict} total order.
Operator {$<$} typically denotes a {strict} total order.
Reference: “Partially Ordered Set,” in _Wikipedia_, June 22, 2024, [https://en.wikipedia.org/w/index.php?title=Partially_ordered_set](https://en.wikipedia.org/w/index.php?title=Partially_ordered_set&oldid=1230452839).
<!--ID: 1723923665330-->
END%%
@ -918,7 +918,7 @@ END%%
%%ANKI
Cloze
A {non-strict} total order satisfies {strong connectivity} whereas a {strict} total order satisfies {connectivity}.
A {1:non-strict} total order satisfies {2:strong connectivity} whereas a {2:strict} total order satisfies {1:connectivity}.
Reference: “Total Order.” In _Wikipedia_, April 9, 2024. [https://en.wikipedia.org/w/index.php?title=Total_order](https://en.wikipedia.org/w/index.php?title=Total_order&oldid=1218090468).
<!--ID: 1723923665333-->
END%%

16
notes/x86-64/registers.md
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@ -238,35 +238,35 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
END%%
%%ANKI
Cloze
Basic
Which register should I use for an 2 byte return value?
Back: `%ax`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1724119420103-->
<!--ID: 1724417749880-->
END%%
%%ANKI
Cloze
Basic
Which register should I use for a 1 byte stack pointer?
Back: `%spl`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1724119420106-->
<!--ID: 1724417749885-->
END%%
%%ANKI
Cloze
Basic
Which register should I use for a 4 byte stack pointer?
Back: `%esp`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1724119420109-->
<!--ID: 1724417749890-->
END%%
%%ANKI
Cloze
Basic
Which register should I use for an 8 byte return value?
Back: `%rax`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1724119420113-->
<!--ID: 1724417749896-->
END%%
%%ANKI