Does $\mathbb{Z}^{+}$ includes zero or not? I think that $0$ is not involved in the set of positive integers, but my book included zero in the set of positive integers in an answer.
The norm of an algebraic integer in an imaginary quadratic integer ring (such as $1 + i$ in $\mathbb {Z} [i]$, for example) is either $0$ or a positive real integer.
Demonstrate that every positive integer can be expressed as the sum of distinct non-negative integer powers of 2. In other words, prove that for every positive integer can be re-written as $2^ {b_0}...
Is my proof that the square root of a positive integer is either an integer or an irrational number correct? The proof goes like this: Suppose an arbitrary number n, where n is non-negative. If $...
Prove that the square root of a positive integer is either an integer ...
(a) If $x \in R, y \in R,$ and $x > 0$, then there is a positive integer $n$ such that $nx > y$. Proof (a) Let $A$ be the set of all $nx$, where $n$ runs through the positive integers.
With your suggested number, you need an integer power of 10 that you can assign 1 as a coefficient to that gives an infinite number of smaller powers of 10 to assign 0 to, in other words, a positive integer that is smaller than an infinite number of positive integers.
The positive integers are $\mathbb Z^+=\ {1,2,3,\dots}$, and it's always like that. The natural numbers have different definitions depending on the book; sometimes the natural numbers are just the positive integers $\mathbb N=\mathbb Z^+$, but other times the natural numbers are actually the non-negative numbers $\mathbb N=\ {0,1,2,\dots}$.