Search results
Results From The WOW.Com Content Network
The model R of real numbers with its usual order and the model Q of rational numbers with its usual order are elementarily equivalent, since they both interpret '<' as an unbounded dense linear ordering.
Two metrics and on X are strongly or bilipschitz equivalent or uniformly equivalent if and only if there exist positive constants and such that, for every ,, (,) (,) (,).In contrast to the sufficient condition for topological equivalence listed above, strong equivalence requires that there is a single set of constants that holds for every pair of points in , rather than potentially different ...
Two rings R and S (associative, with 1) are said to be (Morita) equivalent if there is an equivalence of the category of (left) modules over R, R-Mod, and the category of (left) modules over S, S-Mod. It can be shown that the left module categories R-Mod and S-Mod are equivalent if and only if the right module categories Mod-R and Mod-S are
For example, the natural numbers 2 and 6 have a common factor greater than 1, and 6 and 3 have a common factor greater than 1, but 2 and 3 do not have a common factor greater than 1. The empty relation R (defined so that aRb is never true) on a set X is vacuously symmetric and transitive; however, it is not reflexive (unless X itself is empty).
A ternary / ˈ t ɜːr n ər i / numeral system (also called base 3 or trinary [1]) has three as its base.Analogous to a bit, a ternary digit is a trit (trinary digit).One trit is equivalent to log 2 3 (about 1.58496) bits of information.
Examples of equivalent systems are first- and second-order (in the independent variable) translational, electrical, torsional, fluidic, and caloric systems.Equivalent systems can be used to change large and expensive mechanical, thermal, and fluid systems into a simple, cheaper electrical system.
Instead of "0" and "1" one may use, say, the two possible orientations of the plane R 2 ("clockwise" and "counterclockwise"). It is difficult to choose a canonical rule in this case. It is difficult to choose a canonical rule in this case.
Every element of is a member of the equivalence class []. Every two equivalence classes [] and [] are either equal or disjoint.Therefore, the set of all equivalence classes of forms a partition of : every element of belongs to one and only one equivalence class. [4]