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The ring Z/6Z is reduced, however Z/4Z is not reduced: the class 2 + 4Z is nilpotent. In general, Z/nZ is reduced if and only if n = 0 or n is square-free. If R is a commutative ring and N is its nilradical, then the quotient ring R/N is reduced.
Some studies measure exercise intensity by having subjects perform exercise trials to determine peak power output, [4] which may be measured in watts, heart rate, or average cadence (cycling). This approach attempts to gauge overall workload. An informal method to determine optimal exercise intensity is the talk test.
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables.
A (non-strict) partial order is a binary relation ≤ over a set P which is reflexive, antisymmetric, and transitive. [10] That is, for all a, b, and c in P, it must satisfy the three following clauses: a ≤ a (reflexivity) if a ≤ b and b ≤ a, then a = b (antisymmetry) if a ≤ b and b ≤ c, then a ≤ c (transitivity)
Move 255 10 (2 8 − 1) = 11111111. The largest disk bit is 1, so it is on the final peg (2). All other disks are 1 as well, so they are stacked on top of it. Hence all disks are on the final peg and the puzzle is solved. Move 216 10 = 11011000. The largest disk bit is 1, so disk 8 is on the final peg (2). Note that it sits on base number 11 ...
The Kac–Moody algebras are a large class of infinite-dimensional Lie algebras, say over , with structure much like that of the finite-dimensional simple Lie algebras (such as (,)). The Moyal algebra is an infinite-dimensional Lie algebra that contains all the classical Lie algebras as subalgebras.
The Euclidean distance is the prototypical example of the distance in a metric space, [10] and obeys all the defining properties of a metric space: [11] It is symmetric, meaning that for all points and , (,) = (,). That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is ...
This class may be subdivided into a regular, quasi-regular, or semi-regular polyhedron, and may be convex or starry. The dual is face-transitive and has regular vertices but is not necessarily vertex-transitive. The uniform polyhedra and their duals are traditionally classified according to their degree of symmetry, and whether they are convex ...
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