1 votes 1 votes If $N=(0,1,2,3 ....)$ , then $(N,+)$ is a Group. If $N=(1,2,3 ....)$ , then $(N,+)$ is a not Group. Which one to consider in exam ? Mathematical Logic group-theory discrete-mathematics + – Aspirant asked Feb 6, 2018 retagged Mar 29, 2018 by Sukanya Das Aspirant 369 views answer comment Share Follow See 1 comment See all 1 1 comment reply Devshree Dubey commented Feb 6, 2018 reply Follow Share Look actually N=(0,1,2,3..) why it'll be a group,just consider the properties of a Group. 0 is the additive identity. And in case of multiplication, 1 is the multiplicative identity. Therefore, it is to be considered. However in case of N=(1,2,3...) 1 cannot be used for multiplicative identity. However, since childhood what has been taught is that the range 0-9 comprises of whole numbers. And the range 1-9 is of Natural Numbers. I hope this helps. If you still haven't understood please kindly comment. :) 2 votes 2 votes Please log in or register to add a comment.
1 votes 1 votes Whether or not '0' belongs to the set of natural numbers ℕ is a debatable topic. Although, the definition we've been taught makes a distinction between natural numbers and whole numbers via inclusion or exclusion of zero but still it's always good to mention what definition are we talking about. So, in my opinion, any standard exam will specify the nomenclature it refers to. There can be workarounds like using ℕ+ = {1,2,3, ...} or ℕ0 = ℕ0 = {0, 1, 2, …}. PS: If I were you faced with such a situation, I would have marked it a group because according to Peano Axioms, (the first axiom) - "The constant zero is a natural number". For more information on this refer the WIkipedia page. https://en.wikipedia.org/wiki/Natural_number shashanksingh answered Feb 7, 2018 shashanksingh comment Share Follow See all 0 reply Please log in or register to add a comment.