How To Use Natural number In A Sentence
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Every even natural number x greater than six can be written as the sum of two distinct odd primes.
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Divisibility Test An aid in determining whether a natural number is divisible by another natural number is called a divisibility test.
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It may seem strange to call the natural number system a model.
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It would seem to follow from this principle that enumerative induction is unjustified, since we should not expect (finite) samples from the totality of natural numbers to be indicative of universal properties.
Non-Deductive Methods in Mathematics
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To this effect, consider a hypernatural K in * N that is divisible by every natural number.
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For example in Li's method of writing the sum of the pth powers of the first n natural numbers as sums of binomial coefficients is given.
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Add together the logarithms of aQ the fa&ots, and 'the fum is a logarithm, the natural number correfpond - ing to which will be the produA required.
Encyclopædia britannica;
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They grew so tall, however, and in such preternatural numbers, that she could not see the house at all ---not a chimney pot, not a balcony.
COLDHEART CANYON
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He denoted the number of natural numbers by the transfinite number (pronounced aleph-nought or aleph-null).
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What makes the system exemplify the natural number structure is that it has a one-to-one successor function with an initial object and the system satisfies the induction principle.
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(Newman 1928, 144) To see how this so-called cardinality constraint applies to ramseyfications of theories, note that in Carnap's hands, the non-observational part of reconstructed theories, their theoretical entities, were represented by “purely logico-mathematical entities, e.g. natural numbers, classes of such, classes of classes, etc.”
Vienna Circle
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Cantor conjectured that there are no infinite cardinalities between the size of the natural numbers and the size of the real numbers (and so there are no sets S as described above).
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They grew so tall, however, and in such preternatural numbers, that she could not see the house at all ---not a chimney pot, not a balcony.
COLDHEART CANYON
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If their gcd is not 1, then even using integers you can't reach all natural numbers, so we must have gcd=1.
Number Spanning Using Sets of Natural Numbers
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Often acknowledged in that connection are: his analysis of the notion of continuity, his introduction of the real numbers by means of Dedekind cuts, his formulation of the Dedekind-Peano axioms for the natural numbers, his proof of the categoricity of these axioms, and his contributions to the early development of set theory
Dedekind's Contributions to the Foundations of Mathematics
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These sets are too big to be put into one-to-one correspondence with the natural numbers; they are called uncountably infinite.
Skolem's Paradox
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Italian mathematician Giuseppe Peano axiomatized the mathematical theory of natural numbers.
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The major achievement of the Grundlagen was its presentation of the transfinite numbers as an autonomous and systematic extension of the natural numbers.
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Again it is a theorem of intuitionistic arithmetic that every natural number is either prime or composite.
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Relations needed are, among others, those which assert of a natural number that it codes a sequence, or a formula, or an axiom, or that it is the code, denoted by Sb (ru1 ¦ unZ (x1) ¦ Z (xn)), of a formula obtained from a formula with code r by substituting for its free variable ui the xi th numeral for i = 1,
Kurt Gödel
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Other results obtained by al-Karaji include summing the first n natural numbers, the squares of the first n natural numbers and the cubes of these numbers.
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Ω (mË) says that there is no bijection between the natural numbers and mË.
Skolem's Paradox
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Here are the whole numbers/natural numbers/positive integers up to 700, in binary columns.
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The continuous product of the first 'n' natural numbers is called factorial n and is deonoted by n!
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Thus all infinite sequences of natural numbers have the same power, aleph zero.
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The notes on the keyboard get closer together according to the difference between the sequence of the logarithms of natural numbers.
Times, Sunday Times
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However some important operations may take us outside the realm of the natural numbers-the simplest being subtraction.
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These sets can all be put into one-to-one correspondence with the natural numbers; they are called countably infinite.
Skolem's Paradox
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In this paper, based on the analysis of the genetic algorithm on binary coding, a preliminary discussion is made on the genetic algorithm of natural number coding.
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More precisely, the referential structure in self-referential paradoxes such as the liar is a reflexive relation on a singleton set, whereas the referential structure in Yablo's paradox is isomorphic to the usual less-than ordering on the natural numbers, which is an irreflexive relation.
Self-Reference
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And the second moment gives way to a third, and so on, thus yielding the natural numbers.
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In indirect contexts sense, and not designation, matters and so we may know the well-ordering principle for natural numbers, but not know the principle of mathematical induction because, while they are equivalent in truth value, they have different senses.
Intensional Logic
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Output: meet guess is the natural number two.
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You could think of this correspondence as a buddy system in which each natural number is paired with some positive fraction, and vice versa.
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Frege's approach to providing a logical analysis of cardinality, the natural numbers, infinity and mathematical induction were groundbreaking, and have had a lasting importance within mathematical logic.
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These terms should strictly only be used for the natural numbers or for other countable sets.