Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Since natural numbers($\mathbb{N}$) are set of non-negative integers ... Does it mean that positive integer can be a subset of natural numbers?

For example:

Is {2,3,4} a subset of $\mathbb{N}$?


share|cite|improve this question
Is zero a Natural number? – Hassan Muhammad Nov 3 '11 at 9:32
Yes. Zero is a natural number – xscape Nov 25 '11 at 10:57
up vote 2 down vote accepted

Definition: Let $A,B$ be sets. We say that $A$ is a subset of $B$, if for every $a\in A$ it holds that $a\in B$. If this is the case we write $A\subseteq B$.

Now consider your sets, $A=\{2,3,4\}$ and $B=\{0,1,2,3,4,5\ldots\}=\mathbb N$. For every element in $A$ we have that it is a positive integer, and it is in $B$.

By the definition of inclusion, $A\subseteq B$.

share|cite|improve this answer

If your definition of $\mathbb{N}$ is non-negative integer, then $\mathbb{N}$ is the set $\{0,1,2,3,...\}$. So to answer your question, yes $\{2,3,4,...\}$ is a subset of $\mathbb{N}$ because every element in $\{2,3,4,...\}$ is a non-negative integer.

share|cite|improve this answer
Although the question asked about $\lbrace2,3,4\rbrace$, not $\lbrace2,3,4,\dots\rbrace$. Of course, the answer is still "yes". – Gerry Myerson Nov 3 '11 at 5:32

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.