1 votes 1 votes identity element for (N,+) ,(N ,*) , (Z,* ) ,(R,*) exists? where R=real no N =natural no Z=integer amkrj asked Jun 24, 2015 amkrj 504 views answer comment Share Follow See 1 comment See all 1 1 comment reply vishal8492 commented Jul 20, 2015 reply Follow Share If you define Natural numbers as 0,1,2,3... ThenT0 is identity element for (N+) 0 votes 0 votes Please log in or register to add a comment.
Best answer 2 votes 2 votes identity element is the element in the set which when operated by a number with the operation given produces the same element as result example (N,*) here ) 1 is the identity element as 5(natural number) * 1 = 5 now in your question only (N,+) doesn't have an identity element rest have 1 as the identity element. PS: 0 can be part of $N$ or not and there is no agreement on this. See here. Bhagirathi answered Jun 24, 2015 • selected Aug 20, 2015 by Arjun Bhagirathi comment Share Follow See 1 comment See all 1 1 comment reply akash commented Aug 11, 2015 reply Follow Share for (N,+) isn't 0 is identity element? 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes For (N,+), no identity exists. For all others, identity would be 1. Vivek sharma answered Jun 24, 2015 Vivek sharma comment Share Follow See all 3 Comments See all 3 3 Comments reply anurag panday commented Aug 20, 2015 reply Follow Share a*e=a a+0=a so e=0 is the identity element in some book N=(0,1,2,3...............) in some book N=(1,2,3...........) so in first case there is an identity element is 0 in second case no identity element 1 votes 1 votes Vivek sharma commented Aug 20, 2015 reply Follow Share @anuraj i have also seen this variation in some of the books but most of the questions are solved by excluding 0 0 votes 0 votes anurag panday commented Aug 22, 2015 reply Follow Share yes you are right natural no. has 0 is given in keneth Rosen page no 122 but all of the question are solved by excluding 0 0 votes 0 votes Please log in or register to add a comment.