कभी-कभी गणित में ऐसी क्रियाएँ भी दृष्टिगोचर होती है जब उनमें से एक एक करके दो क्रियाएँ की जाएँ तो फल वही निकलता है, जो उसी प्रकार की एक ही क्रिया से निकल आता है। तनिक इन चार संख्याओं पर विचार करें :
:<math>1, - 1, \sqrt {-1} , -\sqrt{-1} </math>
पंक्ति 11:
[[श्रेणी:समूह सिद्धान्त| ]]
{{अनुवाद}}every group have an special element callad indentity of group and it shows by the symbol 'e'
mathematically e=a is opreted its invers
let we have the set of all integers so it may be griup if and only if when it holds 4 properties which are as follows:
1. closer axiom : let a,b are two element of group so for holding this property a operation b also an element of group;
2.assosiative axiom: a+(b+c)=(a+b)+c
where all above element are in group
3. existence of identity: identity is a such elemet of group which gives the same element when operated with any element of group
aoe=a;
existece of inveres : in group phenomenon invres are the number which gives "e" when they opereted with any element
