Dan Piponi
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 Apr 21 comment Formal Proof that $f^{-1} \circ f = id_x \ , \forall f$ On your second line you have an expression on the left side of an implication and a proposition on the right. Mar 31 comment Number of ways to color paired shoes so that each pair will have different color In the case where three pairs are differently coloured, I think you might not have counted the way you can colour the remaining pair (both of which will have the same colour). Mar 29 comment Differing graphs for simple inverse exponential problem The problem is that there are 9 9th roots of any non-zero number. For positive numbers there's an obvious one that stands out. For negative numbers it's not clear which one you should pick. The real one (like Desmos did) or the first one you meet as you walk anticlockwise around the circle starting at a positive real number (as Mathematica does). Mar 29 comment Differing graphs for simple inverse exponential problem The meaning of the -1/9-th power of a negative number is up for debate. However, I think Google is just plain wrong here :-( Mar 29 comment Gradient of Function If the $x_i$ and $r_i$ are vectors, it's not clear what $(x_i-r_j)^3$ means. What do you mean by the cube of a vector? Mar 29 comment Is $\sqrt{-x^2-\frac{1}{x}}$ a rational function? It's not good enough just to say there can't be a square root. The term inside the square root needs not to be a perfect square. Mar 29 comment Ordinal numbers Yes. See section 5.5 of Nick Higham's book on mathematical style: books.google.com/… Mar 29 comment very basic probability question Did you mean you choose three balls, one from each box? Mar 29 comment Fast algorithm to recognize sortable sequences Mar 28 comment Derivatives of nested/iterated functions. "spiked"? Maybe you meant to type "piqued". Mar 24 comment If ${X_n} < \infty$, then $\sup {X_n} < \infty$, True or False? What range does $n$ live in? Feb 24 comment What are some algorithms that can be used to test if a number is transcendental or not? If you're talking about real numbers represented as a stream of digits, say, being transcendental is not a computable property. Any transcendental number is within $\epsilon$ of a number that isn't transcendental so whatever decision you make, carrying on and reading more digits from the stream could change your decision. Having said that, read en.wikipedia.org/wiki/… for a practical algorithm that can find approximate "small" polynomial equations satisfied by reals. Nov 30 comment Solve complex equation $|z|^5=z^5$ for $z$ $|z|^5$ is $|z^5|$. So first solve $|a|=a$ and then solve $z^5=a$ for all valid $a$. Aug 30 comment Geometric introduction to exterior algebra dl.dropboxusercontent.com/u/828035/Mathematics/forms.pdf Jun 22 comment An easy example of a non-constructive proof without an obvious “fix”? I guess what you mean is that the obvious classical proofs of this proposition can't be fixed. I think there may well be some entirely different constructive proof that hasn't been found yet. Jun 1 comment Real world applications of category theory @Niriel Transition went very well. You can read about the actual project here: theverge.com/2013/9/1/4680456/… May 14 comment How many degrees of freedom would a rotation matrix in R5 have? @loupblanc Yes, quite right. I'll add a comment to the answer. Apr 27 comment Why is $x^0 = 1$ except when $x = 0$? If you're in the combinatorics business, zero is natural. If your business involves primes, zero is not. I'm not sure what people do when they have a foot in both camps. Mar 16 comment Domain of log and its derivative Did you mean to write $(0,\infty)$? The derivative clearly can't exist where the function being differentiated doesn't exist. Mar 12 comment How to explain brackets to young students It sounds like this student has a very good understanding of brackets, something I've seen students struggle with. The problem here isn't with brackets, it's with addition.