43,612 reputation
458129
bio website sites.google.com/site/…
location Fiji
age 38
visits member for 2 years, 8 months
seen 7 hours ago

I'm a lecturer of mathematics at the University of the South Pacific. My research interests are in algebraic topology and metric geometry.


7h
comment Ordered set and ordered field
no, if $x$ and $y$ are different elements, then you can not prove that $x=y$. If you can prove that $x=y$, then of course $x$ and $y$ are the same elements. It is really unclear what you are asking.
12h
comment In a Category, Is the Set of Morphisms Between Objects Defined to Be All Possible Morphisms?
Your title for the question presupposes that the morphisms are taken from some already existing bag of morphisms. This is not the case. The morphisms in a category are not necessarily structure preserving functions. In fact, they don't need to be functions at all. Understanding that should nullify the entire question. You can define a category anyway you like as long as the axioms hold.
1d
comment Bachmann's construction of the real numbers
@sanjab, thanks!! now I just need to brush up on my German.
1d
comment Bachmann's construction of the real numbers
@neptun thank you! This seems to conflict a bit with what is written on page 44, which got me confused.
1d
comment Bachmann's construction of the real numbers
@DanielFischer what you are saying is that this construction by rational intervals can be compared directly to the completion of the rationals by means of minimal Cauchy filters. What I meant by asking if the construction works is whether the details of the proof can be given in terms of that construction, without recursing to other constructions. As an aside question, do you know of a systematic construction of the reals as minimal Cauchy filters of rationals? By that I mean giving an elementary proof of the complete ordered field axioms without using Bourbaki's approach to the reals.
2d
comment Can Aleph Numbers be multiplied?
@mchenja this isn't the place to teach you the very basic facts of the theory of cardinals. You can find plenty of introductory material online or in books that will teach you these things.
Jan
27
comment Can Aleph Numbers be multiplied?
@Axoren I appreciate your comment here however please note that it's not a very constructive one. I deliberately left an explicit bijection from the answer in order to give the reader something to figure out (and it is a very simple detail). The comments to answers are intended to improve the answer, or to address previous comments. I find that your comment is actually not helpful. One should not be spoon-fed.
Jan
27
comment Is complement of a dense set in $\mathbb{R}$ dense in $\mathbb{R}$?
certainly not. $\mathbb R$ is dense in $\mathbb R$ but its complement is not.
Jan
26
comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$
You already have more than one solution.
Jan
26
comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$
@Parhs it was only a hint. The work of turning this into a solution to the problem was left for you. Besides, please avoid leaving meaningless remarks such as "Mr. so and so, who happens to hold a PhD, told me this is really poor, but either did not supply any more criticism, or if any such criticism was supplied I'll just keep it to myself so that I leave a cryptic remark".
Jan
25
comment The powerset of the set of natural numbers - Cantor's Theorem
you won't find any such function because no such function exists because of Cantor's theorem, hence you can't find such a function, as no such functions exists, due to Cantor's theorem...
Jan
23
comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$
think again....
Jan
16
comment Is it possible for it to be impossible to get to work on time?
The question in its current form is too hand-wavy to merit any serious answers other then, with sufficient reformulation of the question, yes, getting to work can be modeled mathematically and depending on the model it may or may not be possible to prove arrival on time.
Jan
15
comment Does the interval notation $[a,b]$ imply that $a<b$?
Yes, $a\le b$ is assumed. Some authors may further assume $a<b$, though most theorems remain true also for intervals of the form $[a,a]$.
Jan
15
comment non-symmetric version of compact = totally bounded + complete
Thanks @MartinSleziak, I had seen this paper and in part precisely that sentence led to this question.
Jan
14
comment If $u$ is a unit, so is $-u$
Write down what it means that $u$ is a unit. Then write down what it means for $-u$ to be a unit. If you do that, you should very quickly find the proof. For future questions do try to show some minimal effort. This type of questions don't really belong on MSE.
Jan
12
comment Linearly Independent Set Proof
what makes you think this claim is even correct?
Jan
5
comment prove that if U is a subspace of the finite dimensional vector space V such that dimU=dimV then U=V
Yes. I think (and that is what I was trying to hint to OP) that precisely that property uses finite dimensionality and must be stated explicitly in the proof.
Jan
5
comment Why isn't $f(x) = x\cos\frac{\pi}{x}$ differentiable at $x=0$, and how do we foresee it?
@Pp.. that would be a good point of view if you were choosing functions at random. But we don't do that and since most functions we look at are infinitely differentiable....
Jan
4
comment Eigenvalue of the substraction of 2 matrices
you need to earn some reputation before you can leave comment. Please read the FAQ section. Also, please avoid posing non-answers as answers (which will promptly be deleted).