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A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment.
An example in Boolos-Burgess-Jeffrey (2002) (pp. 31–32) demonstrates the precision required in a complete specification of an algorithm, in this case to add two numbers: m+n. It is similar to the Stone requirements above. (i) They have discussed the role of "number format" in the computation and selected the "tally notation" to represent numbers:
For example, 13 0 0 has three significant figures (and hence indicates that the number is precise to the nearest ten). Less often, using a closely related convention, the last significant figure of a number may be underlined ; for example, "1 3 00" has two significant figures.
These sciences have been practiced in many cultures from antiquity [5] [6] to modern times. [7] [8] Given their ties to mathematics, the exact sciences are characterized by accurate quantitative expression, precise predictions and/or rigorous methods of testing hypotheses involving quantifiable predictions and measurements. [9]
At the high end is a full ontology that specifies relationships between data elements using precise URIs for relationships and properties. With increased specificity comes increased precision and the ability to use tools to automatically integrate systems, but also increased cost to build and maintain a metadata registry .
Methods have been developed for the analysis of algorithms to obtain such quantitative answers (estimates); for example, an algorithm that adds up the elements of a list of n numbers would have a time requirement of , using big O notation. The algorithm only needs to remember two values: the sum of all the elements so far, and its ...
Use of common words with a meaning that is completely different from their common meaning. For example, a mathematical ring is not related to any other meaning of "ring". Real numbers and imaginary numbers are two sorts of numbers, none being more real or more imaginary than the others. Use of neologisms. For example polynomial, homomorphism.
Surely, there are such cases. Some philosophers say that one should try to come up with a definition that is itself unclear on just those cases. Others say that one has an interest in making his or her definitions more precise than ordinary language, or his or her ordinary concepts, themselves allow; they recommend one advances precising ...