Physlib.Units.ISQDimensionBase

The type `ISQDimensionBase` is an inductive set representing the seven fundamental base quantities of the International System of Quantities (ISQ), as defined in ISO/IEC 80000-1 and the International Vocabulary of Metrology (VIM). These seven mutually independent quantities are: 1. Length ($L$) 2. Mass ($M$) 3. Time ($T$) 4. Electric current ($I$) 5. Thermodynamic temperature ($\Theta$) 6. Amount of substance ($N$) 7. Luminous intensity ($J$) In this system, electric current is treated as a base quantity, making electric charge a derived quantity ($Q = I \cdot T$). This distinguishes it from systems that use charge as a base dimension.

For any two base quantities $q_1, q_2$ in the set of International System of Quantities base dimensions ($\text{ISQDimensionBase}$), it is decidable whether $q_1 = q_2$. The set $\text{ISQDimensionBase}$ contains the seven fundamental quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

The type $\text{ISQDimensionBase}$, which represents the seven fundamental base quantities of the International System of Quantities (length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity), is a finite set.

The International System of Quantities (ISQ) base dimensions set, denoted as $\text{ISQDimensionBase}$, consists of seven mutually independent base quantities: length ($L$), mass ($M$), time ($T$), electric current ($I$), thermodynamic temperature ($\Theta$), amount of substance ($N$), and luminous intensity ($J$). This theorem states that the cardinality (number of elements) of $\text{ISQDimensionBase}$ is equal to $7$.

In the International System of Quantities (ISQ), the dimension of electric charge $Q$ is defined as a derived dimension. It is the product of the base dimension of electric current $I$ and the base dimension of time $T$. Mathematically, this is expressed as $Q = I \cdot T$.

In the International System of Quantities (ISQ), the exponent of the electric current base dimension in the derived dimension of electric charge $Q$ is equal to $1$.

In the International System of Quantities (ISQ), the exponent of the base dimension of time ($T$) in the derived dimension of electric charge ($Q$) is equal to $1$.

In the International System of Quantities (ISQ), the exponent of the base dimension of mass $M$ in the derived dimension of electric charge $Q$ is $0$.

In the International System of Quantities (ISQ), the dimension corresponding to the amount of substance is not equal to the dimensionless identity $1$. Here, the amount of substance is one of the seven independent base quantities, and $1$ represents the dimension where all base quantity exponents are zero.

In the International System of Quantities (ISQ), the dimension corresponding to the base quantity of luminous intensity, denoted as $\text{single}(\text{luminousIntensity})$, is not equal to the dimensionless identity $1$. This confirms that luminous intensity is an independent base dimension in the ISQ framework and cannot be represented as a dimensionless quantity.