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Page "Autocatalytic set" ¶ 49

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Note and trivial

: Note that the equivalence relation generated in this manner can be trivial.

Note that the rules to move-up or pull-down the a, b, or c indexes are trivial, (+......+), so that f abc

Note that the tautology problem for positive Boolean formulae remains co-NP complete, even though the satisfiability problem is trivial, as every positive Boolean formula is satisfiable.

Note that the zero object is the trivial group.

Note that an iterator performs traversal and also gives access to data elements in a container, but does not perform iteration ( i. e., not without some significant liberty taken with that concept or with trivial use of the terminology ).

Note that any character vanishes at 0 except the trivial one, which is 1 on all integers.

Note that if the system basis were not an einselected basis then the last condition is trivial since the disturbed environment is not a function of and we have the trivial disturbed environment basis.

For example, the index of H in G may be countable or uncountable, depending on whether H has a countable number of cosets in G. Note that the index of H is at most the order of G, which is realized for the trivial subgroup, or in fact any subgroup H of infinite cardinality less than that of G.

Note that this means that if the original 3-manifold had in fact a trivial fundamental group, then it is homeomorphic to the 3-sphere ( via the covering map ).

Note that this works equally well when degree ( n ) < degree ( d ); in that case the result is just the trivial ( 0, n ).

Note that in this example the actual next move is essentially irrelevant ; Black has a choice of several relatively trivial ways of delivering instant checkmate.

Note that the transition between " upper " (" contravariant ") and " lower " (" covariant ") vector or tensor components is trivial for a indices ( e. g. ), whereas for μ and ν it is nontrivial, corresponding e. g. to the usual Lorentz signature,.

Note that often the trivial valuation which takes on only the values is explicitly excluded.

Note that it may be not trivial to show that such derived estimator is the unique global maximizer for likelihood function.

Note that the anticommutation relations for the Pauli matrices make the proof of the above defining property trivial.

Note that the set of all attributes is a trivial superkey.

Note that the task of defining ( and counting the number ) of cognate words in the list is far from trivial, and too often is subject to dispute, because cognates do not necessarily look similar, and recognition of cognates presupposes knowledge of the sound laws of the respective languages.

Note that the tangent bundle TJ of J is the trivial bundle J × R and there is a canonical cross-section ι of this bundle such that ι ( t ) = 1 ( or, more precisely, ( t, 1 )) for all t ∈ J.

Finally, we let T ∗ y = z, completing the construction of T ∗.< ref > Verifying that T ∗ is linear trivial .</ ref > Note that T ∗ exists if and only if T is densely defined.

**( Note: it's trivial that every relation in L ( R ) can be uniformized in V, assuming V satisfies AC.

Note that there is a constant added that follows from transition from log-likelihood to ; however, in using the BIC to determine the " best " model the constant becomes trivial.

Note and copy