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The outcome of FH is always a transitive and complete ordering.
However, for each completion of the incomplete preference ordering for each complete ordering that extends the incomplete preference relation the theorem follows.
This does not impose a complete ordering, because in two shafts, there are two filters rather than one, but it can be easily determined which order the two filters should come in.
The document provides a more complete ordering of values, including putting the prevention of harm to humans above protecting property and animals, valuing all human lives equally regardless of categories such as age and race, and possibly "socially and ethically" mandating the use of AVs if they turn out to save lives.
Hence, in contrast to FW, BW always generates a complete ordering of all features.
However, Hilbert R-trees do not expose the complete ordering of spatial data points.
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Theorem 2 Let ( X, d, ⪯ ) be a complete ordered metric space.
Corollary 1 Let ( X, d, ⪯ ) be a complete ordered metric space.
Theorem 4.2 Let ( X, ⪯, ρ ) be a complete ordered modular function space.
In this study, we introduce the concept of externally complete ordered sets.
Then ( X, d ) is a complete ordered cone metric space over a non-normal solid cone.
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