41,016 reputation
452118
bio website sites.google.com/site/…
location Fiji
age 37
visits member for 2 years, 6 months
seen 2 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.


15h
revised Real analysis question: Suprema and Infima
edited title
16h
answered Irrational numbers in between $n$ and $n+1$
2d
comment what is the basic difference between a mapping and a function?
you seem to be asking a different question now. Who said anything about multi-valued anything?
2d
comment what is the basic difference between a mapping and a function?
I'm not sure what that has to do with the question and/or answer.
2d
comment Is binary isomorphic to decimal representation?
very correct. One remark is that you (namely OP) must not confuse the real numbers (which is an abstract structure) and any particular way to representing real numbers. Using any base expansion is just a way to represent numbers. If you have two systems to represent numbers then of course you have a metamorphism from one to the other. It's just the identity.
2d
answered what is the basic difference between a mapping and a function?
Nov
21
comment Why Not Define Connectedness to Mean Path Connected?
the short answer is that perhaps while you have not seen non-artificial examples of connected but not path-connected spaces, there are many situations where a very important space is involved which is quite often connected, but not path-connected.
Nov
20
answered For $A,B,C\subset X$where $X$ is a metric space under some $d$, check if the triangle inequality holds for $d_m(A,B)=\min_{x\in A,y\in B}\{d(x,y)\} $
Nov
20
comment Is a nonzero number infinitely greater than zero?
what is your question?
Nov
20
answered The fixed point in Brouwer's Theorem need not be unique.
Nov
19
comment Showing that $p(x)\mapsto p'(x)$ is not a continous linear transformation
$k$ needs to be some fixed value but for ever $n\in \mathbb N$ you have $\|T(p_n)\|=n$ (emphasis on the "for every").
Nov
18
awarded  Nice Answer
Nov
18
comment Seeking elegant proof why 0 divided by 0 does not equal 1
typically, in a ring, one defined $a/b$ as $a\cdot b^{-1}$, when $b^{-1}$ exists. Then $0/0=0\cdot 0^{-1}$, which would be $0$ if $0^{-1}$ exists. Of course $0^{-1}$ does not exist since by definition this element would solve $0\cdot x = 1$. But $0\cdot x = 0$ and most definitions of ring demand that $0\ne 1$. So, ring theoretically, this is the end of the story.
Nov
18
awarded  definition
Nov
18
comment Seeking elegant proof why 0 divided by 0 does not equal 1
I'm not trying to convince you that $0/0=1$ is a good idea. I know why it does not work. I'm just pointing out that your answer does not address OP's question.
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
your answer only shows that treating $0/0$ as the solution to $x\cdot 0 =0$ does not determine any unique value for $0/0$. That is correct, but does not answer OP's question. OP asked what is inconsistent with defining $0/0=1$. You did not answer that question.
Nov
17
awarded  Nice Answer
Nov
17
answered A sequence $(S_n)$ of reals where Lim inf $(S_n) = -\infty$ and lim sup $(S_n) = +\inf$ and $(S_n)$ is a convergent sequence
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
but perhaps there are compelling reasons then to choose one particular solution as the value of $0/0$. Your argument does not exclude $0/0=1$.
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
as for your later edit, $0/0=1$ is not the case in any ring.