docs: math expressions usage improved in the "Glossary" chapter

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Mateusz Pusz
2023-08-30 18:56:20 +02:00
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@@ -106,7 +106,7 @@
representation of the [dimension](#dimension) for such [quantities](#quantity). representation of the [dimension](#dimension) for such [quantities](#quantity).
The term “quantity of dimension one” reflects the convention in which the symbolic The term “quantity of dimension one” reflects the convention in which the symbolic
representation of the [dimension](#dimension) for such [quantities](#quantity) is representation of the [dimension](#dimension) for such [quantities](#quantity) is
the symbol `1`. the symbol $1$.
- The [measurement units](#unit) and [values](#quantity-value) of quantities of - The [measurement units](#unit) and [values](#quantity-value) of quantities of
dimension one are numbers, but such quantities convey more information than a number. dimension one are numbers, but such quantities convey more information than a number.
- Some quantities of dimension one are defined as the ratios of two - Some quantities of dimension one are defined as the ratios of two
@@ -121,15 +121,16 @@
- Measurement units are designated by conventionally assigned names and symbols. - Measurement units are designated by conventionally assigned names and symbols.
- Measurement units of [quantities](#quantity) of the same [quantity dimension](#dimension) - Measurement units of [quantities](#quantity) of the same [quantity dimension](#dimension)
may be designated by the same name and symbol even when the [quantities](#quantity) are may be designated by the same name and symbol even when the [quantities](#quantity) are
not of the same `kind`. not of the same [kind](#kind).
- For example, joule per kelvin and J/K are respectively the name and symbol of both a - For example, joule per kelvin and J/K are respectively the name and symbol of both a
measurement unit of heat capacity and a measurement unit of entropy, which are generally measurement unit of heat capacity and a measurement unit of entropy, which are generally
not considered to be [quantities of the same kind](#kind). However, in some cases special not considered to be [quantities of the same kind](#kind). However, in some cases special
measurement unit names are restricted to be used with [quantities](#quantity) of specific measurement unit names are restricted to be used with [quantities](#quantity) of specific
[kind](#kind) only. For example, the measurement unit second to the power minus one [kind](#kind) only. For example, the measurement unit second to the power minus one
(1/s) is called hertz (Hz) when used for frequencies and becquerel (Bq) when used for ($\mathsf{1/s}$) is called hertz ($\mathsf{Hz}$) when used for frequencies and
activities of radionuclides. As another example, the joule (J) is used as a unit of becquerel ($\mathsf{Bq}$) when used for activities of radionuclides. As another example,
energy, but never as a unit of moment of force, i.e. the newton metre (N·m). the joule ($\mathsf{J}$) is used as a unit of energy, but never as a unit of moment of
force, i.e. the newton metre ($\mathsf{N·m}$).
- Measurement units of [quantities of dimension one](#dimensionless-quantity) are - Measurement units of [quantities of dimension one](#dimensionless-quantity) are
numbers. In some cases, these measurement units are given special names, e.g. radian, numbers. In some cases, these measurement units are given special names, e.g. radian,
steradian, and decibel, or are expressed by quotients such as millimole per mole equal steradian, and decibel, or are expressed by quotients such as millimole per mole equal
@@ -144,7 +145,7 @@
the centimetre is the base unit of length. the centimetre is the base unit of length.
- A base unit may also serve for a [derived quantity](#derived-quantity) of the same - A base unit may also serve for a [derived quantity](#derived-quantity) of the same
[quantity dimension](#dimension). [quantity dimension](#dimension).
- For number of entities, the number one, symbol `1`, can be regarded as a base unit in - For number of entities, the number one, symbol $1$, can be regarded as a base unit in
any system of units. any system of units.
[`derived unit`](#derived-unit){ #derived-unit } [`derived unit`](#derived-unit){ #derived-unit }
@@ -176,7 +177,7 @@
- For example, the centimetre per second is the coherent derived unit of speed in a CGS system - For example, the centimetre per second is the coherent derived unit of speed in a CGS system
of units but is not a coherent derived unit in the [SI](#si). of units but is not a coherent derived unit in the [SI](#si).
- The coherent derived unit for every [derived quantity of dimension one](#dimensionless-quantity) - The coherent derived unit for every [derived quantity of dimension one](#dimensionless-quantity)
in a given [system of units](#system-of-units) is the number one, symbol `1`. The name and in a given [system of units](#system-of-units) is the number one, symbol $1$. The name and
symbol of the [measurement unit](#unit) one are generally not indicated. symbol of the [measurement unit](#unit) one are generally not indicated.
[`system of units`](#system-of-units){ #system-of-units } [`system of units`](#system-of-units){ #system-of-units }
@@ -199,7 +200,7 @@
[`off-system measurement unit, off-system unit`](#off-system-unit){ #off-system-unit } [`off-system measurement unit, off-system unit`](#off-system-unit){ #off-system-unit }
: - [Measurement unit](#unit) that does not belong to a given [system of units](#system-of-units). : - [Measurement unit](#unit) that does not belong to a given [system of units](#system-of-units).
- For example, the electronvolt (about $1.602\;18 × 10^{19} \mathsf{J}$) is an - For example, the electronvolt (about $1.602\;18 × 10^{19}\;\mathsf{J}$) is an
off-system measurement unit of energy with respect to the [SI](#si). Day, hour, minute off-system measurement unit of energy with respect to the [SI](#si). Day, hour, minute
are off-system measurement units of time with respect to the [SI](#si). are off-system measurement units of time with respect to the [SI](#si).
@@ -213,7 +214,7 @@
[`quantity value, value of a quantity, value`](#quantity-value){ #quantity-value } [`quantity value, value of a quantity, value`](#quantity-value){ #quantity-value }
: - Number and reference together expressing magnitude of a [quantity](#quantity). : - Number and reference together expressing magnitude of a [quantity](#quantity).
- For example, length of a given rod: `5.34 m` or `534 cm`. - For example, length of a given rod: $5.34\;\mathsf{m}$ or $534\;\mathsf{cm}$.
- The number can be complex. - The number can be complex.
- A quantity value can be presented in more than one way. - A quantity value can be presented in more than one way.
- In the case of vector or tensor quantities, each component has a quantity value. - In the case of vector or tensor quantities, each component has a quantity value.
@@ -224,10 +225,10 @@
: - Number in the expression of a [quantity value](#quantity-value), other than any number serving : - Number in the expression of a [quantity value](#quantity-value), other than any number serving
as the reference as the reference
- For example, in an amount-of-substance fraction equal to `3 mmol/mol`, the numerical - For example, in an amount-of-substance fraction equal to $3\;\mathsf{mmol/mol}$, the numerical
quantity value is `3` and the [unit](#unit) is `mmol/mol`. The [unit](#unit) `mmol/mol` quantity value is $3$ and the [unit](#unit) is $\mathsf{mmol/mol}$. The [unit](#unit)
is numerically equal to `0.001`, but this number `0.001` is not part of the numerical $\mathsf{mmol/mol}$ is numerically equal to $0.001$, but this number $0.001$ is not part
quantity value, which remains `3`. of the numerical quantity value, which remains $3$.
[`quantity equation`](#quantity-equation){ #quantity-equation } [`quantity equation`](#quantity-equation){ #quantity-equation }
@@ -250,8 +251,9 @@
: - Mathematical relation between numerical [quantity values](#quantity-value), based on : - Mathematical relation between numerical [quantity values](#quantity-value), based on
a given [quantity equation](#quantity-equation) and specified [measurement units](#unit). a given [quantity equation](#quantity-equation) and specified [measurement units](#unit).
- For example, in the [quantity equation](#quantity-equation) for kinetic energy of a particle, - For example, in the [quantity equation](#quantity-equation) for kinetic energy of a particle,
$T = (1/2) mv^2$, if $m = 2 kg$ and $v = 3 m/s$, then ${T} = (1/2) × 2 × 3^2$ is a numerical $T = (1/2) mv^2$, if $m = 2\;\mathsf{kg}$ and $v = 3\;\mathsf{m/s}$,
value equation giving the numerical value $9$ of $T$ in joules. then ${T} = (1/2)\:×\:2\:×\:3^2$ is a numerical value equation giving the numerical value
$9$ of $T$ in joules.
## Other definitions ## Other definitions
@@ -342,8 +344,8 @@
: - An explicit, known at compile-time, point on an axis of values of a specific [quantity](#quantity) : - An explicit, known at compile-time, point on an axis of values of a specific [quantity](#quantity)
type serving as a reference for other [quantities](#quantity). type serving as a reference for other [quantities](#quantity).
- For example, an ice point is a quantity point with a value of `273.15 K` that is used as - For example, an ice point is a quantity point with a value of $273.15\;\mathsf{K}$ that
the zero point of a degree Celsius scale. is used as the zero point of a degree Celsius scale.
[`quantity point origin`, `point origin`](#point-origin){ #point-origin } [`quantity point origin`, `point origin`](#point-origin){ #point-origin }