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Is the function $f: \mathbb{Q}\to \mathbb{R}$ given by $f(0)=0, ~$$f(r)=\frac{p}{10^q}$ where $p\in \mathbb{Z}$ and $q\in \mathbb{N}$, $(p,q)=1$, one-one and onto?
Since, for $\sqrt{2}\in \mathbb{R}$ there exists no $r\in \mathbb{Q}$ s.t. $f(r)=\sqrt{2}$. There fore the function is not onto....
Resolved: The tags have been removed.
The tags bijectivity, injectivity and surjectivity have been created not so long ago (they are still in the list of new tags.) A natural question is what to do with these tags.
So far the questions about these topics were typically tagged functions and...
There is a question asking about summer programms which is tagged "soft questions" along with other tags. I am not asking about if this question is suitable for math.stackexchange; instead, I am asking about whether the tag "soft question" should be used here.
Description of "soft question":
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