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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
See cstheory.stackexchange.com/a/4098/381
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.