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Dec
1
comment Why not define the Conway base-5 function, instead of base-13?
Oh thank you, I think I get it now, the extra symbol is to code all the negative real numbers. As a logician, I often forget what the "reals" are e.g. that they aren't just $[0,1]$ or $\omega^\omega$ or $2^\omega$ etc.
Nov
25
comment A definition of Conway base-13 function
I don't understand you argument that the function is not computable. You seem to be arguing there is no algorithmic procedure turning an expansion of the input base-13 into an expansion of the output base-10. But if that's your definition of computable, not even multiplication by 3 base-10 to base-10 is computable.
Nov
25
comment Why not define the Conway base-5 function, instead of base-13?
Conway's base 13 always confused me, I never understood why +3 is used rather than +2. Surely he just needs one extra digit for the decimal point, and one extra digit to mark the end of the base-13 prefix? So why didn't we end up with Conway's base 12 function?
Oct
15
answered Calculate the integral of the function only with the immediate integrals
Oct
15
answered What are the elements of $2^A$ if $A$ is a set
Oct
6
comment A Theorem on Compactness By Munkres
By "totally trivial" I don't mean it's obvious. Your question is a good one. I just mean that the difference between this definition and the usual definition is not mathematically significant. It's just a matter of phrasing. Munkres chose this phrasing for the purpose of emphasizing the intrinsic nature of compactness.
Oct
6
comment A Theorem on Compactness By Munkres
This is totally trivial: "open in $X$" just means the intersection of an open set with $X$. "Every open cover has a finite subcover" is entirely equivalent. Munkres is just trying to get away from the habit of thinking of "compact" as being a property of how a set is situated in a larger set, rather than as an intrinsic property.
Oct
6
revised Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc $ then $a|c$.
added 21 characters in body
Oct
6
revised Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc $ then $a|c$.
added 118 characters in body
Oct
6
answered Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc $ then $a|c$.
Oct
6
answered Getting two answers to: How many monoalphabetic substitution ciphers of $\{A,B,C,D\}$ are possible in which no letter is fixed?
Oct
6
answered Limit of the integrals of a $\left\{f_{k}\right\}_{k \in \mathbb{N}}$ decreasing succession of integrable measurable functions,
Oct
5
comment What is $0 \times \infty$?
@fred To the right of all the finite numbers.
Oct
5
awarded  Custodian
Oct
5
reviewed No Action Needed Find a general solution of the reducible second-order differential equation
Oct
5
revised If $n \mid a^2 $, what is the largest $m$ for which $m \mid a$?
made it clearer
Oct
5
reviewed No Action Needed Fleury Algorithm For Eulerian Path proof
Oct
5
suggested approved edit on If $n \mid a^2 $, what is the largest $m$ for which $m \mid a$?
Oct
5
comment If $n \mid a^2 $, what is the largest $m$ for which $m \mid a$?
Presumably the question is this: "Fix $n$ and consider the collection $A_n=\{a : n \mid a^2\}$. What is $\mbox{GCD}(A_n)$?"
Oct
5
revised Prove that if $f$ is increasing then so is $f^{-1}$
edited body