Autosave: 2024-10-18 20:00:02

zk/Additive_inverse_property.md

@@ -3,6 +3,8 @@ tags:
   - theorems
 ---
 
+# Additive inverse property
+
 **Let $a$ represent any member of $\mathbb{Z}$. Then there is a unique member of
 $\mathbb{Z}$ $-a$ such that:**
 

zk/Algebra_key_terms.md

@@ -2,6 +2,8 @@
 tags: [algebra]
 ---
 
+# Algebra key terms
+
 - **Variable**
   - A symbol that stands for a value which may vary
 - **Equation**

zk/Axioms_of_set_theory.md

@@ -4,6 +4,8 @@ tags:
   - theorems
 ---
 
+# Axioms of set theory
+
 The basic notions of set theory are defined in
 [Basic properties of sets](Basic%20properties%20of%20sets.md). There we
 introduced a formal syntax that will be utilised to define the axioms. For easy

zk/Basic_properties_of_sets.md

@@ -3,6 +3,8 @@ tags:
   - set-theory
 ---
 
+# Basic properties of sets
+
 ## Set theory
 
 Set theory is a sub-discipline of both mathematics and formal logic. In

zk/Conjunction_Introduction.md

@@ -4,6 +4,8 @@ tags:
   - logic
 ---
 
+# Conjunction Introduction
+
 If two conjuncts have each been independently derived then they can be
 conjoined. Also known more simply as _Conjunction_
 

zk/Creating_a_Linux_partition_table.md

@@ -1,11 +1,12 @@
 ---
-id: h7f8
 tags:
   - disks
   - Linux
 created: Monday, May 06, 2024
 ---
 
+# Creating a Linux partition table
+
 ## Creating a partition table
 
 To demonstrate the process of partitioning a harddrive I am going to repartition

zk/DRAM_and_SRAM_memory.md

@@ -3,7 +3,7 @@ tags: [memory, hardware]
 created: Friday, July 12, 2024
 ---
 
-# DRAM_and_SRAM_memory
+# DRAM and SRAM memory
 
 There are two types of RAM memory: [SRAM and DRAM](./DRAM_and_SRAM_memory.md).
 

zk/Docker_CLI.md

@@ -6,7 +6,7 @@ tags:
 created: Saturday, March 30, 2024
 ---
 
-# Docker_CLI
+# Docker CLI
 
 ```sh
 # List images

zk/Environmental_and_shell_variables.md

@@ -3,6 +3,8 @@ tags:
   - shell
 ---
 
+# Environmental and shell variables
+
 ## Important!
 
 To understand the difference between environmental and shell variables know
@@ -43,8 +45,7 @@ spawned instances? Is this even possible or do they die on `exit` .
 - The environment is an area that the shell builds every time that it starts a
   session. It contains variables that define system properties.
 
-- Every time a
+- Every time a [shell session](Shell-sessions-e6dd743dec1d4fe3b1ee672c8f9731f6)
-  [shell session](Shell-sessions-e6dd743dec1d4fe3b1ee672c8f9731f6)
   spawns, a process takes place to gather and compile information that should be
   available to the shell process and its child processes. It obtains the data
   for these settings from a variety of different files and settings on the

zk/Equivalent_equations.md

@@ -2,7 +2,7 @@
 tags: [algebra]
 ---
 
-## Equivalent equations
+# Equivalent equations
 
 > Two equations are equivalent if they have the same
 > [solution](Algebra%20key%20terms.md#678811) set.
@@ -30,11 +30,16 @@ of the $=$ symbol). Adding or subtracting the same quantity from both sides
 
 ### Demonstration with addition
 
-$$ x - 4 = 3
 $$
+x - 4 = 3
+$$
+
 The [solution](Algebra%20key%20terms.md#678811) to this equation is $7$
-$$ x -
+
-4 (+4) = 3 (+ 4) $$
+$$
+x -
+4 (+4) = 3 (+ 4)
+$$
 
 Here we have added $4$ to each side of the equation. If $x = 7$ then:
 
@@ -46,11 +51,16 @@ $$ 3 + 4 = 7 $$
 
 ### Demonstration with subtraction
 
-$$ x + 4 = 9
 $$
+x + 4 = 9
+$$
+
 The [solution](Algebra%20key%20terms.md#678811) to this equation is $5$.
-$$ x +
+
-4 (-4) = 9(-4) $$
+$$
+x +
+4 (-4) = 9(-4)
+$$
 
 Here we have subtracted $4$ from each side of the equation. If $x = 5$ then:
 
@@ -62,8 +72,9 @@ $$ 9 - 4 = 5 $$
 
 ### Demonstration with multiplication
 
-$$x \cdot 2 = 10  $$
+$$x \cdot 2 = 10  $$ The [solution](Algebra%20key%20terms.md#678811) to this
-The [solution](Algebra%20key%20terms.md#678811) to this equation is $5$.
+equation is $5$.
+
 $$
 (x \cdot 2) \cdot 3 = 10 \cdot 3 $$ Here we have multiplied each side of the
 equation by $3$. If $x =5$ then
@@ -78,7 +89,12 @@ The [solution](Algebra%20key%20terms.md#678811) to this equation is $6$.
 $$\frac{x
 \cdot 3}{3} = \frac{18}{3}
 $$
+
 Here we have divided each side of the equation by $3$. If $x$ is 6, then
-$$\frac{6
+
-\cdot 3}{3} = 6$$
+$$
+\frac{6
+\cdot 3}{3} = 6
+$$
+
 $$\frac{18}{3} = 6 $$

zk/Equivalent_fractions.md

@@ -4,6 +4,8 @@ tags:
   - fractions
 ---
 
+# Equivalent fractions
+
 Two fractions are equivalent if they represent the same value. To begin with we
 can represent this visually:
 

zk/Expressing_whole_numbers_as_fractions.md

@@ -4,6 +4,8 @@ tags:
   - fractions
 ---
 
+# Expressing whole numbers as fractions
+
 Being asked to express a natural number as a fraction seems confusing at first
 but you need to just know that for any whole number $n$, you express it as a
 fraction with $\frac{n}{1}$.

zk/Factors_and_divisors.md

@@ -3,7 +3,7 @@ tags:
   - prealgebra
 ---
 
-## Factors and divisors
+# Factors and divisors
 
 The terms **factor** and **divisor** are used interchangeably. They are
 different ways of expressing the same mathematical truth and this is because of

zk/Formal_conventions.md

@@ -3,6 +3,8 @@ tags:
   - prealgebra
 ---
 
+# Formal conventions
+
 ## Grouping symbols
 
 We use parentheses to delimit the part of an expression we want evaluated first.
@@ -14,8 +16,10 @@ grouping symbols first,
 We only write one equals sign per line. For example, if we are resolving
 parentheses:
 
-$$ \begin{equation} \begin{split} 2 + \[3 + (4+5)\] = 2 + \[3 +9\] \\ = 2 + 12
+$$
-\\ = 14 \end{split} \end{equation} $$
+\begin{equation} \begin{split} 2 + \[3 + (4+5)\] = 2 + \[3 +9\] \\ = 2 + 12
+\\ = 14 \end{split} \end{equation}
+$$
 
 We call parentheses (`()`), brackets (`[]`) and braces `{}`) grouping symbols.
 When groupings (say parentheses) are used, the expression inside any pair of

zk/Fundamental_Theorem_of_Arithmetic.md

@@ -4,6 +4,8 @@ tags:
   - theorems
 ---
 
+# Fundamental Theorem of Arithmetic
+
 > Every integer greater than one is either a prime number itself or is product
 > of a unique combination of primes.
 

zk/HTTP_request_types.md

@@ -3,6 +3,8 @@ tags:
   - REST
 ---
 
+# HTTP request types
+
 ## GET
 
 - Get data

zk/Increasing_fractions_to_their_highest_terms.md

@@ -4,6 +4,8 @@ tags:
   - fractions
 ---
 
+# Increasing fractions to their highest terms
+
 Given the equivalence between factors and divisors we can increase fractions to
 higher terms in a very similar way to when we reduce fractions. In the latter
 case we are dividing by divisors to reduce. In the former, we are multiplying by

zk/Intro_to_the_Unix_shell.md

@@ -3,6 +3,8 @@ tags:
   - shell
 ---
 
+# Introduction to the Unix shell
+
 ## Unix based systems
 
 Many operating systems are based on the UNIX software architecture. macOS/OSX

zk/Inversion_of_operators.md

@@ -3,17 +3,24 @@ tags:
   - prealgebra
 ---
 
+# Inversion of operators
+
 ## Addition, subtraction
 
 Addition is the inverse of subtraction: $$(x - a) + a = x$$ $$ (6 - 2) + 2 = 6
+
 $$
 
 Subtraction is the inverse of addition: $$(x + a) - a = x$$ $$ (3 + 2) - 2 = 3$$
 
 Division is the inverse of multiplication $$ \frac{a \cdot x}{a} = x$$
 $$ \frac{6
-\cdot 3}{6} = 3$$
+\cdot 3}{6} = 3
+$$
 
 Multiplication is the inverse of division $$ a \cdot \frac{x}{a} = x$$
-$$ 2 \cdot
+
-\frac{8}{2} = 8$$
+$$
+2 \cdot
+\frac{8}{2} = 8
+$$

zk/Invoking_the_shell_in_Python.md

@@ -4,7 +4,7 @@ tags: [python, shell]
 created: Monday, April 29, 2024
 ---
 
-# Invoking the shell_in_Python
+# Invoking the shell in Python
 
 ```py
 import subprocess

zk/Killing_processes.md

@@ -4,6 +4,8 @@ tags:
   - procedural
 ---
 
+# Killing processes
+
 ## Kill a process running on a port
 
 For example a local server.

zk/Listing_and_navigating_directories_in_the_Shell.md

@@ -3,6 +3,8 @@ tags:
   - shell
 ---
 
+# Listing and navigating directories in the shell
+
 ## Listing options
 
 Obviously we know that in order to list the files and sub-directories in our

zk/Magnetic_core_memory.md

@@ -3,7 +3,7 @@ tags: [computer-history, memory]
 created: Friday, September 27, 2024
 ---
 
-# Magnetic_core_memory
+# Magnetic core memory
 
 ![](../img/magnetic-core-memory.jpg)
 

zk/Mainframe_computers.md

@@ -3,7 +3,7 @@ tags: [computer-history]
 created: Friday, September 27, 2024
 ---
 
-# Mainframe_computers
+# Mainframe computers
 
 A mainframe computer, also known as a "big iron" is a high performance computer
 used for resource-intensive tasks that require greater security and availability

zk/Memory_versus_processor.md

@@ -3,7 +3,7 @@ tags: ["question"]
 created: Thursday, August 01, 2024
 ---
 
-# Memory_versus_processor
+# Memory versus processor
 
 > Would a more powerful processor with average or reduced memory capacity
 > perform better than, equal to, or less than a less powerful processor with

zk/Module_wrapping_at_runtime.md

@@ -3,6 +3,8 @@ tags:
   - node-js
 ---
 
+# Module wrapping at runtime in NodeJS
+
 ## The Module Wrapper Function
 
 When Node runs each of our module files are wrapped within an

zk/Natural_numbers.md

@@ -3,6 +3,8 @@ tags:
   - prealgebra
 ---
 
+# Natural numbers
+
 ## The set of natural numbers
 
 $$ \mathbb{N} = {1, 2, 3, ...} $$

zk/Negative_exponents.md

@@ -2,6 +2,8 @@
 tags: [algebra, exponents]
 ---
 
+# Negative exponents
+
 When calculating the exponents of a negative number the answer will always will
 be positive:
 

zk/Network_card.md

@@ -3,7 +3,7 @@ tags: [networks, hardware]
 created: Tuesday, August 06, 2024
 ---
 
-# Network_card
+# Network card
 
 The network card (technically know as the Network Interface Card (NIC)) or
 _network adapter_ is the hardware device that allows a computer to connect to a

zk/Network_hosts.md

@@ -3,7 +3,7 @@ tags: [networks]
 created: Saturday, August 03, 2024
 ---
 
-# Network_hosts
+# Network hosts
 
 A network **host** or **node** is a single computing device attached to a
 ![network](Network_fundamentals.md)

zk/NodeJS_scripts.md

@@ -1,10 +1,9 @@
 ---
-id: 5043
 tags: [node-js]
 created: Friday, April 26, 2024
 ---
 
-# NodeJS_scripts
+# NodeJS scripts
 
 If we want to use NodeJS as a scripting language without going to the trouble of
 setting up an NPM-based development environment, we can use the following

zk/Order_of_operations.md

@@ -3,6 +3,8 @@ tags:
   - prealgebra
 ---
 
+# Order of operations
+
 1. Evaluate expressions in **parentheses**
 1. Evaluate **exponents**
 1. Evaluate **multiplications and divisions** from left to right in the order

zk/Prime_factorization.md

@@ -4,7 +4,7 @@ tags:
   - number-theory
 ---
 
-### Prime factorisation
+# Prime factorisation
 
 Prime factorisation is the activity of expressing a composite number as the
 unique product of [prime numbers](Primes%20and%20composites.md). There are two
@@ -17,8 +17,8 @@ main approaches to this:
 > $n$. We then repeat this process with the resulting factors working
 > recursively until the numbers we are left with are primes.
 
-![Untitled Diagram-Page-1.drawio.png](Untitled%20Diagram-Page-1.drawio.png)
+![Untitled Diagram-Page-1.drawio.png](Untitled%20Diagram-Page-1.drawio.png) _The
-_The prime factors of 27 are 2, 3, 3_
+prime factors of 27 are 2, 3, 3_
 
 it doesn't matter which products we choose as the interim factors, we should
 always reach the same outcome:

zk/Primes_and_composites.md

@@ -4,7 +4,7 @@ tags:
   - number-theory
 ---
 
-## Prime and composite numbers
+# Prime and composite numbers
 
 Definition of a **prime number**:
 

zk/ROM versus disk loading.md

@@ -1,58 +0,0 @@
----
-id: rmvm
-tags: [computer-architecture, memory]
-created: Monday, June 24, 2024
----
-
-# ROM versus disk loading
-
-I will explore the concept via the practical examples of cartridge-based and
-disk-based video games console.
-
-When you insert a disk into an Xbox, the game data is typically read from the
-disk and transferred into the console's memory by the OS. If the game is
-installed to the hard drive, this initially involves transferring substantial
-amounts of data to speed up future access. When you insert a cartridge into a
-console like the SNES, the data is not transferred in the same way. Instead, the
-cartridge contains a ROM chip that, when inserted, integrates directly with the
-motherboard. From the operating system’s point of view, this ROM chip behaves as
-an extension of the system’s memory architecture.
-
-The primary advantage of a ROM-based game is significantly reduced latency. The
-game data can be accessed as rapidly as any other data moving along the buses of
-the motherboard. With a disk, the data must first be read into a buffer and then
-transferred to a memory address where it can be accessed by the CPU.
-
-With a ROM, while the console CPU still uses its own RAM to run the game
-(similar to disk-based systems), the game data on the ROM can be loaded into
-this RAM more quickly because it is directly attached to the motherboard. This
-makes the ROM cartridge effectively a fast, directly connected storage device.
-
-However, despite its speed, the limitation of a ROM cartridge is its storage
-capacity—it can hold only as much data as the chip can accommodate. In contrast,
-a disk can store much more data. This larger storage capacity allows not just
-for bigger and more complex games but also for the possibility of expanding the
-game through additional data downloaded to the console's hard drive. Such
-expansions or patches represent additional data from the console’s storage that,
-combined with the original disk data, are synthesized in memory at runtime for
-enhanced or updated gameplay experiences.
-
-(Note however that modern cartridge-based consoles like the Nintendo Switch can
-also combine ROM-data with expanded data from the console HDD, sourced from the
-internet.)
-
-Both disks and ROMs are forms of static storage in the context of a game
-console. While disks can technically be overwritten with new data, in practice,
-manufacturers implement various locks and protections to prevent this. Any
-changes or additions to the game, such as patches or expansions, are not written
-back to the original disk. Instead, these updates are stored on the console's
-hard drive.
-
-Therefore, if you download an expansion for a game on your Xbox, the original
-disk remains unchanged as when you first purchased it. Consequently, if you were
-to take that disk and load it on another Xbox, it would not include any of the
-expansions or updates. The game would function in its original form, as the
-additional content and updates reside solely on the hard drive of the first
-console where they were downloaded.
-
-## Related notes

zk/ROM_versus_disk_loading.md

@@ -9,22 +9,50 @@ created: Monday, June 24, 2024
 I will explore the concept via the practical examples of cartridge-based and
 disk-based video games console.
 
-When you insert a disk into an XBox, the game data is transferred from the disk
+When you insert a disk into an Xbox, the game data is typically read from the
-into the console's memory by the OS. When you insert a cartridge into a SNES,
+disk and transferred into the console's memory by the OS. If the game is
-there is no transferral of data. The game data is stored on a chip and this chip
+installed to the hard drive, this initially involves transferring substantial
-is attached to the motherboard. From the point of view of the OS, it is just
+amounts of data to speed up future access. When you insert a cartridge into a
-another chip along with the others that comprise the motherboard.
+console like the SNES, the data is not transferred in the same way. Instead, the
+cartridge contains a ROM chip that, when inserted, integrates directly with the
+motherboard. From the operating system’s point of view, this ROM chip behaves as
+an extension of the system’s memory architecture.
 
-The chief advantage with a ROM game is that the latency is greatly reduced. The
+The primary advantage of a ROM-based game is significantly reduced latency. The
-game data can be accessed as rapidly as any other data travelling along the
+game data can be accessed as rapidly as any other data moving along the buses of
-busses of the motherboard. With a disk, the bytes have to be transferred in a
+the motherboard. With a disk, the data must first be read into a buffer and then
-buffer from the disk into a memory address and from there, accessed by the CPU.
+transferred to a memory address where it can be accessed by the CPU.
 
-With a ROM, the console CPU still uses its own memory to run the game (as with
+With a ROM, while the console CPU still uses its own RAM to run the game
-disk-based consoles), it is just that the game data on the ROM can be loaded
+(similar to disk-based systems), the game data on the ROM can be loaded into
-into memory quicker because it is attached to the motherboard.
+this RAM more quickly because it is directly attached to the motherboard. This
+makes the ROM cartridge effectively a fast, directly connected storage device.
 
-becomes part of the motherboard just like the other chips that comprise the
+However, despite its speed, the limitation of a ROM cartridge is its storage
-motherboard.
+capacity—it can hold only as much data as the chip can accommodate. In contrast,
+a disk can store much more data. This larger storage capacity allows not just
+for bigger and more complex games but also for the possibility of expanding the
+game through additional data downloaded to the console's hard drive. Such
+expansions or patches represent additional data from the console’s storage that,
+combined with the original disk data, are synthesized in memory at runtime for
+enhanced or updated gameplay experiences.
+
+(Note however that modern cartridge-based consoles like the Nintendo Switch can
+also combine ROM-data with expanded data from the console HDD, sourced from the
+internet.)
+
+Both disks and ROMs are forms of static storage in the context of a game
+console. While disks can technically be overwritten with new data, in practice,
+manufacturers implement various locks and protections to prevent this. Any
+changes or additions to the game, such as patches or expansions, are not written
+back to the original disk. Instead, these updates are stored on the console's
+hard drive.
+
+Therefore, if you download an expansion for a game on your Xbox, the original
+disk remains unchanged as when you first purchased it. Consequently, if you were
+to take that disk and load it on another Xbox, it would not include any of the
+expansions or updates. The game would function in its original form, as the
+additional content and updates reside solely on the hard drive of the first
+console where they were downloaded.
 
 ## Related notes

zk/Reducing_fractions.md

@@ -4,7 +4,7 @@ tags:
   - fractions
 ---
 
-## Reducing fractions to their lowest terms
+# Reducing fractions to their lowest terms
 
 > A fraction is said to be _reduced to its lowest terms_ if the
 > [greatest common divisor](Factors%20and%20divisors.md#greatest-common-divisor)