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bio website sites.google.com/site/…
location Fiji
age 38
visits member for 2 years, 8 months
seen 52 mins ago

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


3h
comment Cardinality of set $\mathbb{N}^{\mathbb{N}}$ and $\{0,1\}^{\mathbb{N}}$
It's not quite right to say that every function $f\colon \mathbb N \to \{0,1\}$ is also a function $f\colon \mathbb N \to \mathbb N$.
4h
comment Cardinality of set $\mathbb{N}^{\mathbb{N}}$ and $\{0,1\}^{\mathbb{N}}$
Welcome to SE. Please note that this site is not aimed at answering your homework questions or otherwise for you to just dump questions and wait for an answer. You are supposed to show some effort, tell us what you tried, where you got stuck, what is the context of the questions etc.
16h
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.
21h
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
revised Bachmann's construction of the real numbers
deleted 96 characters in body; edited title
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.
1d
asked Bachmann's construction of the real numbers
Jan
29
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
revised Can Aleph Numbers be multiplied?
edited body
Jan
27
answered Can Aleph Numbers be multiplied?
Jan
27
answered Surprising applications of topology
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
24
answered Extending Taylor's theorem from one to several variables
Jan
23
comment Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$
think again....