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 Sep 25 comment Is every injective function invertible? which is to say, it is invertible on its image. $f^{-1}: f(A) \longrightarrow A$. May 23 comment Tangent of a Straight Line @J.Roberts "I think of a tangent intersecting the equation at one point," and it does... one point and a line of points. May 23 comment How is a symmetric group the subgroup of the group of isometries of three-dimensional space? So you have an isomorphism from $S_4$ to "rotations of the cube". How are you supposed to consider $S_4$ other than as rotations of the cube? This question seems a little vague! Mar 22 comment Commutator subgroup - or? Is there a typo here, $\alpha(a^{-1})a$ is just $\alpha$...? Oct 27 comment find $\dim X\times \mathbb{P}^{2}$ @spencer What's the definition of times? May 12 comment Should every group be a monoid, or should no group be a monoid? Is Definition 2 also incorrect/insufficient (for similar reasons to Definition 2'?) Nov 14 comment Is this an open problem? I don't see why we only consider primes? oeis.org/A069035 Nov 14 comment Is this an open problem? @Salahuddin not really, just a subsequence of this: oeis.org/A069035 Aug 21 comment Why $\mathbb{Z}_p^*$ is a cyclic group? Um, $\mathbb{Z}_2 \times \mathbb{Z}_3$ is abelian, but $2\nmid 3$. Aug 21 comment Why $\mathbb{Z}_p^*$ is a cyclic group? Please could you elaborate on the final sentence? Aug 21 comment find $\dim X\times \mathbb{P}^{2}$ What have you tried so far? Isn't $dim(X \times Y)=dim(X)+dim(Y)$? So aren't you really only asking what is $dim(X)$? Aug 20 comment Why isn't math on the sine of angles the same as math on the angles in degrees? @nbubis In which case linear does not imply additive, see examples above. :) Aug 20 comment Why isn't math on the sine of angles the same as math on the angles in degrees? @nbubis Take care, it's not true for f(x)=1 or f(x)=x+1, as these are "affine" rather than "linear". Jul 18 comment Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ @celtschk haha, ok my bad, what I really meant to say was "how can you say that without doing some kind of calculation". Jul 18 comment Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ @celtschk I wouldn't say that is any more obvious that the difference of two squares. Jul 18 comment Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ So you're not using "then $x^3 \neq y^3$ in line 2 at all, this was the confusing bit. I now see what you are trying to say in the last part, well done. Jul 18 comment Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ @Exile.90 You are implicitly using the fact the $f(x)=x^3+x$ is increasing, this needs to be demonstrated or at least mentioned. Your argument seems to use $a \neq b$ and $c \neq d$ $\implies$ a+c $\neq$ b+d (which is not true). Jul 18 comment Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ You're saying that $x=y$ doesn't imply $x^3=y^3$, i.e. cubed isn't function over the complex numbers?? You're wrong. Jul 18 comment Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ @Brad How would you know that: ( x^2+y^2+xy+1 =/= 0) without doing the difference of two squares calculation? Mar 12 comment Cauchy Sequence that Does Not Converge @Michael surely every sequence can be thought of as a series?