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


Oct
3
answered Set of continuous functions as a ring
Oct
3
comment Quick and painless definition of the set of real numbers
The equivalence relation you refer to is a totally different one than the one using, e.g., Cauchy sequences. Primarily, you don't need the axiom of choice to choose one representative from each equivalence class, since there is a canonical one. With Cauchy sequences there is no canonical choice of representative. With the uniform completion, you can first look at all Cauchy filters, and define an equivalence relation. The nice thing is that with the filters there is a minimality condition that chooses for you a unique representative from each equivalence class.
Oct
3
comment Quick and painless definition of the set of real numbers
obviously, the arithmetic operation will take this into account. This is not the real issue with this definition. In particular, this definition can be used to define the reals. The details of the proofs though are almost horrific.
Oct
3
comment Prove that every element is a pth power in a cyclic group
Bezout supplies you with as many $k$'s as you need.
Oct
3
answered Quick and painless definition of the set of real numbers
Oct
3
answered Why is probability taught after a first course in calculus?
Oct
3
answered Prove that every element is a pth power in a cyclic group
Sep
30
answered GCD's and how they generate groups
Sep
30
awarded  Refiner
Sep
30
awarded  Explainer
Sep
30
comment Probability paradox: Mario's dice game
assuming you meant "over a discrete infinite set" then yes, that is very correct.
Sep
30
comment Probability paradox: Mario's dice game
Try to describe a uniform distribution on $\mathbb N$. Saying $p(x)=0$ for every $x\in \mathbb N$ does not describe a probability distribution since the probabilities have to add-up to $1$.
Sep
30
comment Probability paradox: Mario's dice game
There is no such thing as "pick randomly". You have to specify the probability distribution. Usually, when saying "pick randomly" one means "pick using the uniform distribution". However, there is no such thing as a uniform distribution on an infinite discrete set, which is often the cause to many 'paradoxes'.
Sep
30
comment Probability paradox: Mario's dice game
since you did not specify how Mario splits his infinitely many guests into groups, you can't possible determine the probability of you belonging to a specific group and thus you can't perform any computation.
Sep
29
answered Is there a typo this theorem in Munkres's Topology? If not please explain
Sep
29
answered Proving that two quotient groups are isomorphic
Sep
28
answered Let $(X,d)$ be a metric space. Let $U \subseteq (X,d)$. Let $k \in (X,d)$. Prove…
Sep
28
answered What are some useful alternative notations in mathematics?
Sep
28
revised Why does the harmonic series diverge but the p-harmonic series converge
added 1 character in body
Sep
28
awarded  Nice Answer