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Centimetre–gram–second system of units; CGS system of units; Chinese units of measurement; Coherence (units of measurement) Comparison of the imperial and US customary measurement systems; Composition of Yards and Perches; Conventional electrical unit
Then let E 1 denote the set of global units ε that map to U 1 via the diagonal embedding of the global units in E. Since E 1 is a finite-index subgroup of the global units, it is an abelian group of rank r 1 + r 2 − 1. The p-adic regulator is the determinant of the matrix formed by the p-adic logarithms of the generators of this group.
One difference between the Gaussian and SI systems is in the factor 4π in various formulas that relate the quantities that they define. With SI electromagnetic units, called rationalized, [3] [4] Maxwell's equations have no explicit factors of 4π in the formulae, whereas the inverse-square force laws – Coulomb's law and the Biot–Savart law – do have a factor of 4π attached to the r 2.
Dirichlet's unit theorem shows that the unit group has rank 1 exactly when the number field is a real quadratic field, a complex cubic field, or a totally imaginary quartic field. When the unit group has rank ≥ 1, a basis of it modulo its torsion is called a fundamental system of units. [1]
When that multiplier is one, the unit is called a coherent derived unit. For example, the coherent derived SI unit of velocity is the metre per second, with the symbol m/s. [1]: 139 The base and coherent derived units of the SI together form a coherent system of units (the set of coherent SI units). A useful property of a coherent system is ...
A system of units of measurement, ... For example, where the unit of length is the metre; a distance of 1 metre is 1,000 millimetres, or 0.001 kilometres.
In mathematics and related fields, an abstract structure is a way of describing a set of mathematical objects and the relationships between them, focusing on the essential rules and properties rather than any specific meaning or example. [1] [2]
A geometrized unit system [1] or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, c, and the gravitational constant, G, are set equal to unity. = = The geometrized unit system is not a completely defined system.