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 Mar 16 answered The number of real roots of $x^5 + 2x^3 + x^2 + 2 = 0$ is Mar 12 comment The Third Derivative @probablyme Point taken. I guess I was just surprised that you didn't learn about this particular application when you learned about derivatives in Calculus, because in my Calc. classes we did a fair amount of applications to different things. Mar 10 awarded Yearling Mar 10 comment The Third Derivative @probablyme You're an applied math major but you can't vouch for an elementary property of the derivative? Mar 10 awarded Talkative Mar 10 comment The Third Derivative @1089 If you can explain what is confusing I will try to clarify. Mar 10 answered The Third Derivative Feb 1 awarded Popular Question Oct 15 comment Completion of rational numbers via Cauchy sequences What do you mean "maybe"? Is this property somehow equivalent to transitivity as I stated above? Oct 15 comment Completion of rational numbers via Cauchy sequences Why is Definition 1 property 1 called transitivity? Doesn't transitivity mean that $\forall x,y,z \in K : (x \leq y \land y \leq z) \implies x \leq z$? Sep 24 awarded Autobiographer Aug 25 awarded Informed Aug 19 awarded Tumbleweed Feb 4 comment Russell's Paradox in *Naive Set Theory* by Paul Halmos @GME: that helps me understand somewhat. However, I still can't see how we know that we can't assume $B \notin A$ and then contrive some other contradiction. Help? Jan 26 revised Russell's Paradox in *Naive Set Theory* by Paul Halmos deleted 36 characters in body Jan 26 asked Russell's Paradox in *Naive Set Theory* by Paul Halmos Jan 9 revised Can we always construct an element not on a list? added 97 characters in body Jan 9 asked Can we always construct an element not on a list? Jan 7 comment The language of abstract algebra in $ab=a, ab=b$ implies $a=b$ I have no trouble applying this principle to objects which are somehow explicitly constructed. However, in this case, $a$, $b$, and $ab$ do not seem to me to be explicitly constructed and so I have trouble applying the principle. Jan 7 comment The language of abstract algebra in $ab=a, ab=b$ implies $a=b$ So you are referring to the ambiguity between a function and the category theoretic notion of a morphism? I haven't studied category theory yet, but maybe it would help me with this problem?