Bill Dubuque
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 11h comment Has there ever been an application of dividing by zero? @hobbs For polynomials$f(x)$ the limit can be eliminated. Instead simply evaluate at $h = 0\,$ after cancelling $h.\,$ This yields a purely algebraic definition of the derivative of a polynomial, see here. 15h revised cancelling out before evaluation of variable added 12 characters in body 15h revised gcd of $x$ and $2$ in $\mathbb Z[x]$ added 1891 characters in body 1d answered If $a$ and $b$ are nonzero integers such that each is a divisor of the other, show that $a = ± b$ . 1d comment Find all $g(x)$ such that $f(g(x))=g(f(x))$ A classic result of Ritt gives a complete answer for polynomials and rational functions. 1d comment If $p$ and $q$ are positive prime numbers such that $p$ is divisible by $q$, show that $p = q$. Which definition of "prime" are you using? 1d comment gcd of $x$ and $2$ in $\mathbb Z[x]$ @user26857 I disagree, esp. considering that an analogous answer received over 100 votes. 1d comment Determining if $A(B(x))$ is a formal power series The downvote is quite puzzling. Please do explain. 1d answered gcd of $x$ and $2$ in $\mathbb Z[x]$ 1d answered No irreducible element in a UFD can be a square. 1d comment Determining if $A(B(x))$ is a formal power series I see no restriction to the "basic ring axioms" in the question. In fact they OP asks "what other techniques....". Those are precisely the techniques that I link to. I think your answer is highly misleading even after the edit so I have downvoted it. There is, alas, a lot of confusion about this topic, even among professional mathematicians (e.g. see the deleted answer in the linked thread), so I think it is essential to be very careful not to further add to this widespread confusion. 1d comment Question about the infinite products of formal power series See this answer for the appropriate notion of convergence. 1d comment Convergence of formal power series substitution See this answer for the appropriate notion of convergence. 1d comment Convergence of formal power series substitution See this answer for the appropriate notion of convergence. 1d comment Closed form of generating function consisting of power of two binomials See this answer for the appropriate notion of convergence. 1d comment Closed form of generating function consisting of power of two binomials See this answer for the appropriate notion of convergence. 1d comment When variable substituitions are allowed in Taylor's Polynomials and when they aren't? See this answer for the appropriate notion of convergence. 1d comment Explanation of the composition of two formal power series See this answer for the appropriate notion of convergence. 1d comment Explanation of the composition of two formal power series See this answer for the appropriate notion of convergence. 1d comment Defining composition of two formal series - what is going on? @Elaqqad See this answer for the appropriate notion of convergence.