| 词汇 | example_english_natural-number |
| 释义 | Examples of natural numberThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. If k is a naturalnumber such that 2 ! It has a naturalnumber m as argument whose meaning is the number of unpacked arguments which are waiting in the stack. We use indices for that: an exception constructor (or simply an exception) is the name of a data type, possibly indexed by a naturalnumber. In our example, each object of type naturalnumber has four modes: plus, minus, times and divide. There exists a naturalnumber s such that the following is true. Because any naturalnumber multiplied by two always equals an even number, all the guests wind up in even-numbered rooms. Let m be a naturalnumber such that m < 0 /10. The ' naturalnumber ' approach is only one way to allow multivalued features. The function at denotes list indexing and rev k computes the bit-reversal of a naturalnumber. The functor preserves finite products and the naturalnumber object (up to isomorphism). Each of these events also carries a naturalnumber as a parameter. If such a naturalnumber does not exist, we say that the degree of is infinite. The predicate that decides whether a naturalnumber is even or not may be defined as follows. Similarly, rational numbers are traditionally formalised as pairs consisting of an integer, and a positive naturalnumber. As an added benefit, proofs - naturally tree-structured - need not be arbitrarily linearized just so that naturalnumber recursion and induction can be performed on them. Of course, this can be easily repaired, by considering level mappings that map each naturalnumber to itself. If indexed, every possible naturalnumber would be written onto some book. Let be a naturalnumber to be chosen later. The assertion says that u, which denotes a procedure, always doubles the content of an argument, which should be a reference storing a naturalnumber. We represent the pointer by the state of a cell containing a naturalnumber. Alternately, one can formalize the notion of naturalnumber within the theory, thus allowing for a finite axiomatization, albeit possibly also capturing non-standard natural numbers. In connection with part (iv), it is worth observing why preserves the naturalnumber object. Observe that the typing rules for constructors and datatypes are indexed by a naturalnumber. It is true, of course, that one cannot create a new naturalnumber and add it to the set of all natural numbers. It follows that each data value must contain a tag (usually a naturalnumber) which distinguishes from each other the constructors of the relevant data type. Now let m be any naturalnumber. By requiring hash to be an injection we are assuming that no two keys will map to the same naturalnumber and hence avoid the problem of clashes. The naturalnumber for a subject committee would be larger. From the Hansard archive Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0 Here, "n" may be any naturalnumber or infinity. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Even-order harmonics and odd-order harmonics are both naturalnumber multiples of the input frequency. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The factorial number system provides a unique representation for each naturalnumber, with the given restriction on the digits used. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. An ordinal notation is an effective description of a countable ordinal by a naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A set is infinite if and only if for every naturalnumber the set has a subset whose cardinality is that naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since this formula holds for every naturalnumber k the overspill principle forces it to hold for some nonstandard element n. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The notation "na" (where "n" is a naturalnumber) stands for the group sum of "n" copies of "a". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Lagrange, for example, had shown that any naturalnumber can be expressed as the sum of four squares. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These functions take "n" arguments for some naturalnumber "n" and are called "n" -ary. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The naturalnumber following 0 is 1 and no naturalnumber precedes 0. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. And, since every naturalnumber can be trivially represented as a real number, therefore the real numbers are "no less than" countable. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. By convention, a calendar year consists of a naturalnumber of days. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In combination with zero, successor allows one to name any naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. He used q-series to prove that any naturalnumber can be represented as a sum of an even square and two triangular numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Naturally, this 2-adic integer has no corresponding naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. He proved that every naturalnumber is a sum of four squares. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Under second quantization, multiparticle excitations are considered; these are given by log "n" for any naturalnumber "n". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The naturalnumber is known as the degree of the polynomial. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The cardinality of a finite set is a naturalnumber the number of elements in the set. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For example, every naturalnumber is the sum of at most 4 squares, 9 cubes, or 19 fourth powers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. More formally, a naturalnumber is the equivalence class of all sets under the equivalence relation of equinumerosity. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A functor with a superscript "n", "n" a naturalnumber 1, denotes "n" consecutive applications (iterations) of that functor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The simplest numeral system is the unary numeral system, in which every naturalnumber is represented by a corresponding number of symbols. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A semiperfect number is a naturalnumber that is equal to the sum of all or some of its proper divisors. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These behave as discrete analogs of integration and differentiation, only for series (functions of a naturalnumber) instead of functions of a real variable. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The greatest common divisor "g" is the largest naturalnumber that divides both "a" and "b" without leaving a remainder. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A naturalnumber is divisible by three if the sum of its digits in base 10 is divisible by 3. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. When "k" is a naturalnumber, this problem is normally viewed as computing the number of "k" -colorings of a given graph. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Zero is a naturalnumber, and if n is a naturalnumber, then suc n is a naturalnumber too. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. When a naturalnumber is used as a set, this is typically what is meant. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Mathematical induction, as formalized in the second-order axiom above, works because "k" is used to represent an "arbitrary" naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If is a naturalnumber, then 1 and divide without remainder. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For example, in arithmetic, it allows the expression of the statement that every naturalnumber has a successor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. As a weak counterexample, suppose ("x") is some decidable predicate of a naturalnumber such that it is not known whether any "x" satisfies. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A consequence of this definition is that every naturalnumber is equal to the set of all preceding natural numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Here there is a digit at every hypernatural rank rather than merely a digit for every rank given by a naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. On the other hand, does not have a maximum since there is no largest naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since any naturalnumber can be factored into powers of primes, it suffices to prove the theorem for prime numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Exponentiation to the power of any naturalnumber other than zero can be defined consistently whenever multiplication is power-associative. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The binomial theorem (tear off the leg that says that the exponent has to be a naturalnumber) is a good example. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Every finite word has a length, which is, obviously, a naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is possible to effectively decide whether a given naturalnumber is prime by testing every possible nontrivial factor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If "n" is a naturalnumber, then "x" is the "n" th pentagonal number. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A counter stores a single naturalnumber (initially zero) and can be arbitrarily long. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. But the concept of naturalnumber is already assumed for the iteration. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. However, due to the virtual nature of the count, it need not be a naturalnumber, as one might expect a count to be. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Continue this process until all elements of the set have been assigned a naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This result can be established for "n" a naturalnumber by induction, or using integration by substitution. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A total order on the natural numbers is defined by letting if and only if there exists another naturalnumber "c" with "b". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The second part of the program nondeterministically chooses a naturalnumber on request. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This is clearly true; it just asserts that every naturalnumber has a square. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Given a naturalnumber, the index of the multiplicative group of the -th powers of the non-zero elements of in is finite. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A multiset corresponds to an ordinary set if the multiplicity of every element is one (as opposed to some larger naturalnumber). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Throughout this article the word number refers to a naturalnumber. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. One frequent division notion, a naturalnumber of equal parts, is known as "partition" to educators. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. No naturalnumber other than 1 divides both 6 and 35, since they have no prime factors in common. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The brute-force algorithm examines every naturalnumber less than 1000 and keeps a running sum of those meeting the criteria. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. They are usually written in upper-case and with a naturalnumber as exponent to indicate the order. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Informally, each naturalnumber "n" is defined as the set whose members each have "n" elements. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. One may visualize a two-dimensional array with one column and one row for each naturalnumber, as indicated in the table above. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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