set

Question

identity element for (N,+) ,(N ,*) , (Z,* ) ,(R,*) exists?

where R=real no

N =natural no

Z=integer

Comments

If you define Natural numbers as 0,1,2,3... 

ThenT0 is identity element for (N+) 

Answer 1

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. 

Comments

for (N,+) isn't 0 is identity element?

Answer 2

For (N,+), no identity exists. For all others, identity would be 1.

Comments

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   

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@anuraj i have also seen this variation in some of the books but most of the questions are solved by excluding 0

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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