The law of trichotomy holds for cardinal numbers, so that any two sets are either equinumerous, or one has a strictly smaller cardinality than the other.
32.
And as such, pro-placoderm experts consider Pseudopetalichthyida to be the sister group of the Arthrodires + Phyllolepida + Antiarchi trichotomy and the Acanthothoraci + Rhenanida dichotomy.
33.
Writing about planar affine mapping, Rafael Artzy made a similar trichotomy of planar, linear mapping in his book " Linear Geometry " ( 1965 ).
34.
In Zermelo Fraenkel set theory and Bernays set theory, the law of trichotomy holds between the cardinal numbers of well-orderable sets even without the axiom of choice.
35.
In classical logic, this "'axiom of trichotomy "'holds for ordinary comparison between real numbers and therefore also for comparisons between integers and between rational numbers.
36.
Already in the 1879 " Begriffsschrift " important preliminary theorems, for example a generalized form of law of trichotomy, were derived within what Frege understood to be pure logic.
37.
The claim is therefore complicated by disputes over what renders a village a " town ", the usual trichotomy in current use of British English being village, town or city.
38.
Genesis 2 : 7 " rather implies than asserts the trichotomy of spirit, soul, and body " and must be " illuminated by the light of subsequent Scriptures " to reveal its full import.
39.
Banfi and colleagues ( 2011 ) have suggested that the phylogenetic trichotomy of this genus " Allium " " sensu lato " is sufficiently distinct as to warrant splitting it into three separate genera.
40.
Some theologians believe that Apollinaris himself, however, confused the Pauline trichotomy with the Platonic trichotomy by confounding the " pneuma " ( " ru ah " ) with the " nous ".
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