That freedom proves to be equivalent to another freedom, known as "active" general covariance.
For some service operations, the SRPostCondition of an operation may happen to match (or be equivalent to) another's SRPreCondition.
It would be important to consider the actual type of mutation (and not just which gene was mutated), since in a particular gene, one type of mutation may not be equivalent to another type.
Yet if Mr. Cunningham's basic precept is that any movement is equivalent to another, that does not mean his dance works merely make up a collection of steps and gestures.
To do so, a mathematician would have to show that NP-complete problems are equivalent to another class of problem, P problems, in which complexity grows relatively slowly with the number of terms.
The first one is the Paretian condition that an alternative is equivalent to another when all individuals are indifferent between them.
In [75] it is proved that Petty's conjectured projection inequality is equivalent to another open problem (namely the isoperimetric problem for the Holmes-Thompson measure) over the class of origin-symmetric convex bodies, since the following statement is proved there.
Hawthorne (2005) raises the possibility that, in the course of grasping that p entails q, S will cease to know p. He also notes that SP1 is defensible on the (deviant) assumption that a thought, p, is equivalent to another, q, if p and q hold in all of the same possible worlds.
In fact, the norm (|cdot|) is equivalent to another norm (|cdot|_{E} ) defined by |u|_{E}: = biggl int_{Omega}|Delta u|^{2}, dx biggr)^{frac{1}{2}} on E, i.e., there exist two positive constants (C^), (C^) such that C^ |u|leq|u|_{E}leq C^|u|.
Assume that f is (Delta_{H} -differentiable, we say tH} -differentiable})-differentiable in the sense (i) or (mathrm{(i)}Delta_{H})-differentiable if, in the definition of (Delta_{H})-derivative, gH-difference is equivalent to H-difference, and we say that f is (Delta_{H} -differentiable in tH} -differentiablemathrm{(in)}Delthe{H})-differentiable if gH-difference isenseivalent toranother case.
The symmetrization E of a quasi-Banach ideal lattice E of measurable functions on I="(0,a), 0<a⩽∞, or I= N, consists of all functions with decreasing rearrangement belonging to E. For an order continuous E we show that every subsymmetric basic sequence in E which converges to zero in measure is equivalent to another one in the cone of positive decreasing elements in E, and conversely.
