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1d
comment Has the Collatz Conjecture been proven to be unprovable?
@BeansonToast: Here's the Makholm Conjecture: Take any positive integer; if it is 1 then add 1, otherwise subtract 1. Repeat this process ad infinitum. I conjecture that you will always eventually reach 1 no matter which positive integer you start out with. Would the reasoning you champion lead to the conclusion that it is impossible to prove the Makholm Conjecture under any set of axioms? If not, then what's the difference between Makholm and Collatz that makes you accept the reasoning for one of them but not the other?
2d
comment Deriving Euler's theorem from Fermat's little theorem
@SimonZhu: Please think just a little bit for yourself. If you have $a^{(p-1)k+1}\equiv a\pmod p$ and want $a^{(p-1)(q-1)+1}\equiv a\pmod p$, then at least start by comparing the two equations and find out what the difference is. The difference is that one says $k$ where the other says $q-1$. Was $k$ arbitrary? Yes it was. Is $q-1$ a possible value for an aribitrary integer? Yes it is.
2d
comment Deriving Euler's theorem from Fermat's little theorem
@Thomas: As I said, he's asking two questions in the body. The latter of those two questions is exactly what is also asked in the question title, and I see no reason at all to assume that this second question doesn't mean what it says (both in the title and in the body).
2d
comment Deriving Euler's theorem from Fermat's little theorem
@Thomas: What makes you conclude he's "using Euler's theorem in a non-standard way"? Note that he's asking two questions separated by "and also", not one question phrased in two different ways.
2d
answered Deriving Euler's theorem from Fermat's little theorem
2d
comment The relation x=1
It may help the imagination to "unfold" the definition: "$(x,y)\in R$ iff $x=1$" means that $R$ is the set $$\{(1,0),(1,1),(1,2),(1,3),\ldots,(1,8273),\ldots,(1,\pi),(1,-42),(1,\frac5{17}‌​),(1,\sqrt2),\ldots\}$$
2d
revised The relation x=1
edited tags
2d
answered Prove that the Mandelbrot Set Is A Closed Set
2d
answered Why would the cubic have $5$ roots?
2d
comment Finding the functions for circular reflection and their inverted forms
@hohner: Who says that? I'm saying that $\frac1{x^2+y^2}x=\frac x{x^2+y^2}$.
2d
comment Finding the functions for circular reflection and their inverted forms
@hohner: $(x',y')=\lambda(x,y)$ and $\lambda=\frac{1}{x^2+y^2}$, so $x'=\lambda x=\frac{1}{x^2+y^2}x=\frac{x}{x^2+y^2}$.
2d
comment Finding the functions for circular reflection and their inverted forms
@hohner: Yes, it will. Remember that $(x',y')=\lambda(x,y)$, so the numerator comes from this multiplication.
2d
comment Finding the functions for circular reflection and their inverted forms
x @hohner: Yes!
2d
comment Finding the functions for circular reflection and their inverted forms
For finding the inverse function, note that the criterion for "the image of $P$ is $P'$" is symmetric in $P$ and $P'$ -- that is, inversion in a circle is its own inverse!
2d
comment choose from implication and logical and in write assertions in first-order logic
The second one is not well-formed at all -- there's an "if" with no matching "then".
2d
answered Trying to understand a part of the RSA algorithm…
2d
comment Please Help me understand this proof
@TaylorTed: No, because the second given is a statement about the intersection of the sets in $\mathcal F$, whereas the goal is a statement about the union of the sets in $\mathcal G$. The intersection and union unfold to different quantifiers.
2d
comment $\liminf_n \min(a_n,b_n)=\min( \liminf_n a_n, \liminf_n b_n)$
x @jordan: If you're writing for mathematicians, you don't need to reference that result. You can safely assume that the reader is able to see on his own that it is true.
2d
revised Is $\frac00=\infty$? And what is $\frac10$? Are they same? Does it hold true for any constant $a$ in $\frac{a}0$
missing dollar sign
2d
comment $\liminf_n \min(a_n,b_n)=\min( \liminf_n a_n, \liminf_n b_n)$
It should take at most a dozen lines to prove it with freshman-course levels of rigor and detail. Any reader who cares to follow references will probably be able to construct that proof in his head anyway. What do you need a reference for?