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He is noted as the first to publish an arithmetical theory of irrational numbers.
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An arithmetical formula may have free set variables and bound individual variables.
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We use here arithmetical models because they are like the models of management accounting, illustrative and easily understood and applied in practice.
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In a special test of written arithmetical operations (addition, subtraction, multiplication, and division), and initial score of 0/20 was obtain.
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A set is recursive if and only if it is at level of the arithmetical hierarchy.
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Not every implicitly arithmetical set is arithmetical, however.
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Even when fractional numbers can be represented exactly in arithmetical form, errors will be introduced if those arithmetical values are rounded or truncated.
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By choosing cards it answered arithmetical problems and spelled out words.
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A formula with no bound set variables (that is, no quantifiers over set variables) is called arithmetical.
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These identities, like the identities between the series, yield arithmetical convolution identities involving the sum-of-divisor function.
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