Sentence examples for defined as equivalence from inspiring English sources

Ordinal numbers are defined as equivalence classes of well-orderings under similarity.

The overall architecture of their system is very much like that of the early dynamic systems discussed above, only indifference relations are no longer defined as equivalence relations, but rather as reflexive and symmetric (not necessarily transitive) relations.

For mean change from baseline in average eye IOP at all time points in the ITT population, the upper and lower 95% CI limits were within a 1.0 mm Hg margin at each hour, which was the prespecified margin defined as equivalence.

In the ITT population, the upper and lower 95% CI limits for mean change from baseline in worse eye IOP at week 12 were within a 1.0 mm Hg margin at each hour, and within the prespecified 1.5 mm Hg margin defined as equivalence.

As mentioned above, a projective geometry \ \Pi\) may be defined as an equivalence class of affine geometries, that is, an equivalence class of projectively related affine connections [\ \Gamma\)].

For example, in the usual construction of the ring of integers, an integer is defined as an equivalence class of pairs (m,n) of natural numbers, where (m,n) is equivalent to (m′,n′) if and only if m + n′ = m′ + n.

Hence, projective geometry may be defined as an equivalence class of affine geometries.

A path is therefore sometimes defined as an equivalence class of curves under arbitrary parameter transformations.

Usually it is defined as the equivalence relation (or: the reflexive relation) satisfying Leibniz's Law, the principle of the indiscernibility of identicals, that if x is identical with y then everything true of x is true of y.

"The rational numbers can be formally defined as the equivalence classes of the quotient set (Z × (Z {0})) / ~, where the Cartesian product Z × (Z {0}) is the set of all ordered pairs (m,n) where m and n are integers, n is not zero (n ≠ 0), and "~" is the equivalence relation defined by (m 1,n 1) ~ (m 2,n 2) if, and only if, m 1 n 2 − m 2 n 1 = 0".

The study was defined as an equivalence study for the primary outcome.