Is there a bijection from $A = ]0,1[$ to $B = A \cup \{1,2,3,4\}$? If there is, give example. I had this question on exam few days ago, and I have been googling for days, but I can't find a solution. I think (probably wrong) that there is not because $A$ is subset of $B$, but I am totally u...
Related to the question Proof that Laplacian is surjective $\mathcal{P}^n\to\mathcal{P}^{n-2}$, in the only answer of this question, @uncookedfalcon explain that, by the inductive hypothesis, the second term of $$ x^{M-1} y^- z^- = \Delta(x^{M+1} y^- z^-) - x^{M+1}\Delta(y^- z^-)$$ lies in the im...
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/or elementary-set-theory. Considering tha...
What on Earth is the tag algebraic-identities for? It seems to me that questions containing at least one equal sign get randomly tagged with it, including questions that have nothing to do with algebra. The tag excerpt (there's no tag wiki) mentions "algebraic structures", which I guess includes ...
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