Question

Is \[Z + \] the same as \[N\] ?

Answer 1

Hint: The symbol \[Z + \] represents all the integers whereas the symbol \[N\] represents all the natural numbers . The positive sign after the \[Z\] symbol represents all the positive integers . Both the symbols represent a set corresponding to their representation .

Complete step-by-step answer:
\[Z\] stands for “ Zahlen “ , which in German means numbers . When putting a \[ + \] sign at the top , it means only the positive whole numbers , starting from 1 , then 2 and so on up to infinite . \[Z\] usually does not denote the set of positive integers, but rather the set of non - negative integers .
\[N\] is used to represent the set of all the natural numbers \[\left\{ {1,2,3,4,5.....} \right\}\] , starting from \[1\] to infinite . The set of natural numbers which is represented by \[N\] is the subset of \[Z\] , but only contains elements as positive natural numbers .
On comparing we find that both the symbols are different but are both the different sets which contain the same elements .
Therefore , we can assume that \[Z + \] and \[N\] are the same .

Note: In the set of \[Z + \] do not include the number \[0\] , as it is a neutral number rather than a positive number , for reference the positive sign in the symbol \[Z + \] , is representing the positive numbers only . For natural numbers , the sum of two natural numbers and the product of two natural numbers is always a natural number , but this does not apply for division and subtraction . For example
\[2 \times 4 = 8\] , but
\[\dfrac{2}{4} = 0.5\] .