Question Number 114807 by Eric002 last updated on 21/Sep/20

is zero a natural number 0∈N?

Commented byMJS_new last updated on 21/Sep/20

there seem to be two different definitions  of N, both are in use... confusion...  old definition N={1, 2, 3, ...}; N∪{0}=N_0   new definition N={0, 1, 2, ...}; N\{0}=N^★   so the answer depends on in which country  and on which school you are    when I was in school (a zillion years ago) we  leaned these things one after the other:  (1) N: as you count (nobody would start to       count by 0).  (1.1) addition is always possible in N  (1.2) multiplication is always possible in N       but n×1=n  (1.3) substraction only as a test of addition       a+b=c ⇒ c−b=a∧c−a=b  (1.4) substraction a−b possible only if a>b?  ⇒  (2) Z=N∪{...−2, −1, 0} these are magical       numbers we need to substract without limits       a−b=x always solveable in Z  (2.1) 0 neutral element of addition  (2.2) 1 neutral element of multiplication    then Q (a÷b=x solveable), then R (all non−  periodic numbers like (√2), π; later e...),  finally C

Commented byEric002 last updated on 21/Sep/20

thank you for explaning but what is the  difference between N and N^∗

Commented byMJS_new last updated on 21/Sep/20

the old N is the same as the new N^★   ={1, 2, 3, ...}    the old N_0  is the same as the new N  ={0, 1, 2, ...}

Commented byEric002 last updated on 21/Sep/20

thank you sir

Commented byRasheed.Sindhi last updated on 21/Sep/20

Why isn′t there any international  institute which play roll in this  connection? Which make  standards so that  such  confusions be killed?

Commented byMJS_new last updated on 21/Sep/20

standards are no longer accepted in the age  of internet; everybody′s own opinion counts  more than any standard

Commented byRasheed.Sindhi last updated on 21/Sep/20

ThankSs Sir!