奇偶性 (数学)




在數學中，奇偶性是對於整數的一種性質，每個整數都可被分為奇數或偶數：可被2{displaystyle 2}2整除者是偶數，不可被2{displaystyle 2}2整除者是奇數。


偶數定義為所有形如2k{displaystyle 2k}2k的整數，其中k是整數：


{2k∣k∈Z}{displaystyle {2kmid kin mathbb {Z} }}{displaystyle {2kmid kin mathbb {Z} }}

而奇數定義為所有形如2k+1{displaystyle 2k+1}{displaystyle 2k+1}的整數，其中k是整數：


{2k+1∣k∈Z}{displaystyle {2k+1mid kin mathbb {Z} }}{displaystyle {2k+1mid kin mathbb {Z} }}

上述的奇偶性僅適用於整數，因此12,4.201{displaystyle {frac {1}{2}},4.201}{displaystyle {frac {1}{2}},4.201}等並不適用。




目录






  • 1 加法和減法


  • 2 乘法


  • 3 除法


    • 3.1 被除數比除數有較多2的因數


    • 3.2 被除數比除數有相同數量2的因數


    • 3.3 被除數比除數有較少數量2的因數




  • 4 参考文献


  • 5 參見





加法和減法



  • 奇數±{displaystyle pm }pm奇數={displaystyle =}=偶數

  • 奇數±{displaystyle pm }pm偶數={displaystyle =}=奇數

  • 偶數±{displaystyle pm }pm偶數={displaystyle =}=偶數



乘法



  • 奇數×{displaystyle times }times奇數={displaystyle =}=奇數

  • 奇數×{displaystyle times }times偶數={displaystyle =}=偶數

  • 偶數×{displaystyle times }times偶數={displaystyle =}=偶數



除法


奇數除以任何一個整數（不論偶數抑或奇數），其商並非必然是奇數或偶數，亦沒有一定規律。偶數情況亦然。例如：


  • 1（被除數是奇） ÷ 3（除數是奇） = 0.3（非整數，非偶亦非奇）

設商是整數，若被除數比除數有較多2的因數，商會是偶數。



被除數比除數有較多2的因數



  • 12（被除數 = 2×2×3） ÷ 3（除數 = 3） = 4（偶數）

  • 500（被除數 = 2×2×5×5×5） ÷ 2（除數 = 2） = 250（偶數）



被除數比除數有相同數量2的因數



  • 500（被除數 = 2×2×5×5×5） ÷ 100（除數 = 2×2×5×5） = 5（奇數）

  • 408（被除數 = 2×2×2×51） ÷ 500（除數 = 2×2×5×5×5） = 0.816（非整數，非偶亦非奇）



被除數比除數有較少數量2的因數



  • 12（被除數 = 2×2×3） ÷ 8（除數 = 2×2×2） = 1.5（非整數，非偶亦非奇）

  • 136（被除數 = 2×2×2×17） ÷ 32（除數 = 2×2×2×2×2） = 4.25（非整數，非偶亦非奇）



参考文献





參見




  • 函数的奇偶性

  • 置换的奇偶性




Comments

Post a Comment

Popular posts from this blog

Information security

Image
This article is part of a series on Information security Related security categories Internet security Cyberwarfare Computer security Mobile security Network security Threats Computer crime Vulnerability Eavesdropping Malware Spyware Ransomware Trojans Viruses Worms Rootkits Bootkits Keyloggers Screen scrapers Exploits Backdoors Logic bombs Payloads Denial of service Defenses Computer access control Application security Antivirus software Secure coding Secure by default Secure by design Secure operating systems Authentication Multi-factor authentication Authorization Data-centric security Encryption Firewall Intrusion detection system Mobile secure gateway Runtime application self-protection (RASP) v t e Information security , sometimes shortened to InfoSec , is the practice of preventing unauthorized access, use, disclosure, disruption, modification, inspection, recording or destruction of information. Th...
Read more

Volkswagen Group MQB platform

Image
The Volkswagen Group MQB platform is the company's strategy for shared modular design construction of its transverse, front-engine, front-wheel-drive layout (optional front-engine, four-wheel-drive layout) automobiles. Volkswagen spent roughly $60bn [1] developing this new platform and the cars employing it. The platform underpins a wide range of cars from the supermini class to the mid size SUV class. MQB allows Volkswagen to assemble any of its cars based on this platform across all of its MQB ready factories. This allows the Volkswagen group flexibility to shift production as needed between its different factories. Beginning in 2012, Volkswagen Group marketed the strategy under the code name MQB , which stands for Modularer Querbaukasten , translating from German to "Modular Transversal Toolkit" or "Modular Transverse Matrix". [2] [3] MQB is one strategy within VW's overall MB (Modularer Baukasten or modular matrix) program which also includes th...
Read more

Daniel Guggenheim

Image
Daniel Guggenheim 1925 photo Born ( 1856-07-09 ) July 9, 1856 Philadelphia, Pennsylvania Died September 28, 1930 (1930-09-28) (aged 74) Port Washington, New York Alma mater Peirce College Known for Battle for control of ASARCO Daniel Guggenheim Medal Spouse(s) Florence Shloss Children Meyer Robert Guggenheim Harry Guggenheim Gladys Eleanor Guggenheim Parent(s) Meyer Guggenheim Barbara Guggenheim Daniel Guggenheim, 1910 Daniel Guggenheim (July 9, 1856 – September 28, 1930) was an American mining magnate and philanthropist, and a son of Meyer and Barbara Guggenheim. Contents 1 Biography 2 Personal life 2.1 Aviation 2.2 Alaska 3 See also 4 References 5 Further reading 6 External links Biography Born and raised in Philadelphia, Daniel Guggenheim was sent to Switzerland as a young man to study the Swiss lace and embroidery business, and to serve as a buyer for his father's import firm. The...
Read more