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Oct
18
comment What is the purpose of showing some numbers exist?
:D @Potato (thanks!)
Oct
18
awarded  Nice Answer
Oct
18
answered Looking for Proofs Of Basic Properties Of Real Numbers
Oct
17
answered What is the purpose of showing some numbers exist?
Oct
17
answered Generalization of metric spaces?
Oct
17
comment Using the “open cover” definition of compactness to show that $[0,1]$ is compact
did you open up a topology book (e.g., Munkres) and read the proof?
Oct
17
comment How many sets of cardinality $n$ there are in the $\mathcal{P}(S)$ if $|S|=m$?
read about the binomial coefficients ${n \choose k} = \frac{n!}{k!(n-k)!}$.
Oct
15
comment If Ax = 0 for every x in $R^n$, A is a zero matrix
Let $A\ne 0$ be an arbitrary metric satisfying the stated property. We may assume the entry $a_{ij}\ne 0$. But then ... contradicting the given property of the matrix.
Oct
15
comment Characteristic of a ring
what is the finite characteristic property? Do you simply mean that the ring has finite characteristic? what is infinite characteristic then?
Oct
15
answered If Ax = 0 for every x in $R^n$, A is a zero matrix
Oct
14
answered Dimensions in geometry
Oct
14
answered Almost everywhere agreement (Hyperreals)
Oct
13
comment Is there an established name for this kind of function composition?
none that I know of.
Oct
13
answered Is there an established name for this kind of function composition?
Oct
13
comment Is Topological Space an Algebraic Structure?
@ZhenLin wouldn't you consider, say, monoid objects in Rel with respect to the tensor product given by the cartesian product of sets to be algebraic structures? I don't see why multivaluedness means non-algebraic.
Oct
13
comment Is Topological Space an Algebraic Structure?
@ZhenLin why is that a big stretch?
Oct
13
comment Is Topological Space an Algebraic Structure?
It is a beautiful result. I'm not sure it's alchemy. Basically, a Hausdorff compact topological space is algebraic in the sense that to any ultrafilter in it (which must converge to a unique point), there is associated a point in the space (the limit!). This is very much like an infinitary algebraic operation. Getting rid of the compact just requires some careful tinkering with the ultrafilter monad.
Oct
13
answered Is Topological Space an Algebraic Structure?
Oct
13
reviewed Leave Open Finding bounds for $\sin(x) \cos(x)$?
Oct
13
reviewed Close Find the number of points in $(-\infty,\infty)$ for which $x^2-x\sin x-\cos x=0.$