이항연산,binary_operation

Child:
덧셈,addition
뺄셈,subtraction
곱셈,multiplication
나눗셈,division
이상 가감승제 사칙연산 연산,operation
{
가 +sum
감 −difference
승 ×product
제 ÷quotient
이건 체,field 관련인데 관계 TBW.
}
지수,exponentiation

and, nand
or, nor
배타적_논리합,exclusive_or,XOR, xnor
{
2의 자리(carry)는 버리는 덧셈으로 생각해 버리면 편하다.
}

벡터,vector의:
스칼라곱,scalar_product,dot_product
내적,inner_product .....벡터와 벡터를 연산했는데 벡터가 아니라 실수이므로, 이항연산 아니라고.[1]
벡터곱,vector_product,cross_product
외적,outer_product

관련 법칙들:
교환법칙,commutativity
결합법칙,associativity
분배법칙,distributivity

Notation (표기법,notation):
네이버 사전 - 통일 안됨.. 도대체 어디서 나온 표현들인지? 나는 이렇게 알고 있는데.. en etc
이랑 표현 중위 표기법 infix_notation
접두 부호 표현 전위 표기법 prefix_notation AKA Polish notation
후치 표기법 후위 표기법 postfix_notation AKA reverse Polish notation, 후치 표기법
중위 표기법에는 괄호,parenthesis가 필요하지만 전위 후위는 없어도 ok인가? CHK
[https]수학백과: 전위표기법 AKA 폴란드 표기법(Polish notation) - 리스프,Lisp, S-표현식 S-expression
WpKo:폴란드_표기법
[https]수학백과: 중위표기법
WpKo:중위_표기법
[https]수학백과: 후위표기법 AKA 역 폴란드 표기법(reverse Polish notation) RPN - 스택,stack 포스,Forth
WpKo:역폴란드_표기법
이항연산에서 ...CHK
전위 연산자 피연산자1 피연산자2
중위 피연산자1 연산자 피연산자2
후위 피연산자1 피연산자2 연산자
함수 연산함수명(피연산자1, 피연산자2)

binary와 비슷한 단어: dyadic
차이는?

분류방법이..?
곱셈과 나눗셈 둘은 스케일링 scaling 관련으로 묶을 수 있음. scale scaler
관련 scalar_multiplication WpKo:스칼라_곱셈

[edit]

정의

집합 $S$ 상의 이항연산: $S$ 의 임의의 두 원소로 이루어진 순서쌍 $(a,b)$ 에 대하여 $S$ 의 원소를 하나 대응시키는 법칙. 그 원소를 $a\ast b$ 라고 쓰면, $S$ 상의 이항연산 $\ast$ 은 다음 함수
$\ast:S\times S\to S$
$(a,b)\mapsto a\ast b\in S$
여기서 $S\times S$ 는 모든 순서쌍 $(a,b)$ 들의 집합.
$S\times S=\{(a,b)|a\in S,b\in S\}$

(고급수학.pdf p24)

군,group페이지의 정의 중 '10개의 특강으로~' 책 내용도 참조.

이항연산,binary_operation에서 교환법칙,commutativity이 성립하는 군,group은 가환군,commutative_group(=아벨군).

https://freshrimpsushi.github.io/posts/magma-in-abstract-algebra/
대수학,algebra esp 추상대수,abstract_algebra학 적 관점. Easy.
rel. 마그마,magma - 마그마는 집합,set에 대한 닫힘성,closedness과 이항연산으로 간단하게 정의됨

MKLINK:
이항연산과 마그마,magma, 모노이드,monoid와의 관계. 다음 글 참조:
이항연산과 모노이드(Binary operations and Monoid)
https://gosamy.tistory.com/364


See also:
산술,arithmetic#s-3도 참조. 거기서 옮겨올것. TODO


Up:
연산,operation
이항 이진 binary ...pagename 바이너리,binary? and 둘,two
----

Warning: fopen(./data/cache/backlinks/a/ac/ac7472507c713f10cc96d5994d183098) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/b/b8/b8d21ac76d73211515d3a4e73d9b869e) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/6/6a/6a16efc795aa011ee2758d99315c16ae) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/c/c8/c888927d7333a1c0b97be97a00dc44a1) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/e/e4/e4d4f1c2a73c1fcb1391c0e2291549c8) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/9/93/93156500f0ce443aff05455348b4ccb1) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/e/e9/e9df5a37baa509fffbae18b207a5eb9a) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/b/bb/bbe37abab2af73788b7010450bd25772) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/b/b1/b1290726b43243bcd8ef626e676f9fa4) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/f/f0/f08f31ab99bccf35fba083460e0c09df) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/d/d9/d9f5d3a28f0aa8c8c2d7c866eed42f65) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/d/d8/d8cb5c24145b5a9dad456ac67d546d65) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/a/ae/ae04696e88a04c4a741b72aec8bc34bb) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/7/76/76cc22062c2d9885209fb3621e637234) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/9/99/991503cdbbb7a18e830a1096bd876456) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/d/dd/dd22bdeb133012140ca5d6d4d4c2a4bd) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/e/e1/e1e9f46c9f3dbcc21dae9d82e4dfa75c) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/a/a9/a9dbbcc0ce6cc0a071e59f13bc068a62) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/a/a9/a9bb2fbcbfb9959aae536781bc3e3247) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/a/a0/a04c87e2b94593583e501e0261b8c3ad) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/e/e1/e1088744e7eaaf2ffcc7b497e9c46604) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/e/ef/ef13c0d51829a61d225784bfb5dd86e0) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/8/8b/8be6d21290e3590977ad20057b7767fe) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/e/e6/e601a220c6bb662054ca7e1ead11150b) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/f/fd/fd314fc8e3fd2e0d3826c9c44f715e7b) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277

Warning: fopen(./data/cache/backlinks/c/c0/c0e663adabb1e71b3d2b1c7d5adb7950) [function.fopen]: failed to open stream: No such file or directory in /home1/tomoyo/public_html/123/lib/cache.text.php on line 277