通州文艺志愿者参加2017区社会组织同享汇活动

百度李想认为，无人驾驶将是人工智能最早的一个大规模商业应用，汽车商业模式也会彻底改变，按单车售价的买卖交易将演变成按里程进行交易。

In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by S, so S(n) = n?+?1. For example, S(1) = 2 and S(2) = 3. The successor function is one of the basic components used to build a primitive recursive function.

Successor operations are also known as zeration in the context of a zeroth hyperoperation: H₀(a, b) = 1?+?b. In this context, the extension of zeration is addition, which is defined as repeated succession.

Overview

The successor function is part of the formal language used to state the Peano axioms, which formalise the structure of the natural numbers. In this formalisation, the successor function is a primitive operation on the natural numbers, in terms of which the standard natural numbers and addition are defined.^[1] For example, 1 is defined to be S(0), and addition on natural numbers is defined recursively by:

m + 0	= m,
m + S(n)	= S(m + n).

This can be used to compute the addition of any two natural numbers. For example, 5 + 2 = 5 + S(1) = S(5 + 1) = S(5 + S(0)) = S(S(5 + 0)) = S(S(5)) = S(6) = 7.

Several constructions of the natural numbers within set theory have been proposed. For example, John von Neumann constructs the number 0 as the empty set {}, and the successor of n, S(n), as the set n?∪?{n}. The axiom of infinity then guarantees the existence of a set that contains 0 and is closed with respect to S. The smallest such set is denoted by N, and its members are called natural numbers.^[2]

The successor function is the level-0 foundation of the infinite Grzegorczyk hierarchy of hyperoperations, used to build addition, multiplication, exponentiation, tetration, etc. It was studied in 1986 in an investigation involving generalization of the pattern for hyperoperations.^[3]

It is also one of the primitive functions used in the characterization of computability by recursive functions.

References

^ Steffen, Bernhard; Rüthing, Oliver; Huth, Michael (2018). Mathematical Foundations of Advanced Informatics—Volume 1: Inductive Approaches. Springer. p.?121. doi:10.1007/978-3-319-68397-3. ISBN?978-3-319-68397-3.
^ Halmos, Chapter 11
^ Rubtsov, C.A.; Romerio, G.F. (2004). "Ackermann's Function and New Arithmetical Operations" (PDF).

Paul R. Halmos (1968). Naive Set Theory. Nostrand.

?

This mathematical logic-related article is a stub. You can help Wikipedia by expanding it.

[1] Steffen, Bernhard; Rüthing, Oliver; Huth, Michael (2018). Mathematical Foundations of Advanced Informatics—Volume 1: Inductive Approaches. Springer. p.?121. doi:10.1007/978-3-319-68397-3. ISBN?978-3-319-68397-3.

[2] Halmos, Chapter 11

[Ackermann-3] Rubtsov, C.A.; Romerio, G.F. (2004). "Ackermann's Function and New Arithmetical Operations" (PDF).

[1]

[2]

[3]

低血压吃什么药	鹿参膏有什么作用和功效	西梅是什么水果	隼读什么	点了斑不能吃什么
张国荣为什么喜欢男的	刷牙时牙龈出血是什么原因	心里难受是什么原因	柿子与什么食物相克	黄芪补什么
uv是什么	白酒泡什么补肾壮阳最好	被孤立的一般是什么人	透亮是什么意思	五十岁叫什么之年
为什么口臭	高诊是什么意思	双非是什么意思	鲶鱼吃什么食物	高半胱氨酸是什么意思

下面有味道用什么药hcv8jop7ns1r.cn	痔瘘和痔疮有什么区别cl108k.com	脱发看什么科xinmaowt.com	怀孕可以吃什么水果hcv8jop2ns0r.cn	胃炎吃什么药最有效hcv9jop4ns5r.cn
肺部肿瘤切除后吃什么hcv9jop6ns8r.cn	什么是美尼尔氏综合症hcv9jop2ns6r.cn	孕妇可以喝什么饮料hcv7jop6ns9r.cn	宫腔内偏强回声是什么意思hcv8jop3ns6r.cn	人参和什么泡酒壮阳hcv9jop1ns8r.cn
头七需要做什么hcv9jop4ns1r.cn	苹果花是什么颜色hcv7jop6ns7r.cn	吃什么补肺养肺比较好hcv9jop6ns4r.cn	宝宝不长肉是什么原因hcv8jop4ns9r.cn	恶寒发热是什么意思hcv8jop3ns4r.cn
预防更年期提前应该吃点什么药hcv8jop6ns2r.cn	预防医学是干什么的hcv8jop0ns4r.cn	spao是什么牌子hcv8jop2ns7r.cn	ak是什么hcv7jop6ns6r.cn	搬家有什么讲究和忌讳hcv9jop4ns1r.cn

通州文艺志愿者参加2017区社会组织同享汇活动

Overview

See also

References