The notion of equality of functions is equality of functions qua sets, which, under the standard principle of extensionality of sets, entails that two functions are equal precisely when they contain the same ordered pairs.
Hence, the displayed thoracic layer does not necessarily equal the corresponding anatomic layer, and the visualised impedance changes do not match precisely with their localization within the thorax.
Her degree of entrenchment for the proposition that Vienna is the capital of Austria equals n precisely if she stops disbelieving that Vienna is the capital of Austria after n people have passed by and told her it is.
Consequently, the flat dimension of a Leavitt path algebra L K ( E ) equals 1 precisely when L K ( E ) is not von Neumann regular (i.e., when there are L K ( E ) -modules which are not flat).
In this way, preference structures can be determined more precisely or with equal precision but smaller sample size.
It was why much of the British left, once dogmatically anti-European, swung the other way with equal fervour precisely because it now seemed to offer more security to ordinary people.
Of course, political states are still required to treat their constituents as free and equal citizens precisely because the volenti principle is generally irrelevant to relations among compatriots.
A decoding mapping, denoted by, associates with a syndrome a vector of Hamming weight less than or equal to, which syndrome is precisely equal to, and.
Bins contained roughly equal numbers of introns; precisely equally sized bins were unobtainable, due to a relatively large number of introns that fell on the bin thresholds, particularly for short introns in dipterans.
Supply and demand between each pair of currencies would not be precisely equal every day.
