Is this proposition true?
$\mathbb R \nsubseteq \mathbb N $
It may seem trivial, but I want to be sure. Also would the simple "not subset" operator without the "not equal" part be more suitable?
$\endgroup$1 Answer
$\begingroup$We write $A\subseteq B$ if every $a$ which is an element of $A$ is an element of $B$. If $A\subseteq B$ and $A\neq B$ we write $A\subsetneq B$ (and sometimes $A\subset B$, although that may denote possible equality as well).
If we write $A\nsubseteq B$ then we mean that $A$ is not a subset of $B$. This means that there exists some $a\in A$ such that $a\notin B$.
Now, is $\Bbb{R\subseteq N}$ or not?
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