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location Fiji
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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.


2d
comment What problems arise when using infinitesimals in calculus?
the reason mathematicians considered infinitesimals as absurd was for a very different reason than initial objections to negative or complex numbers. For the latter there was no problem in presenting formal systems with such numbers, but these new numbers went against the intuition of mathematicians, born by prejudice perhaps. With infinitesimals it is quite the other way around. The intuition was there since Newton, and perhaps earlier. However, until Robinson, no one was able to present a formal system with infinitesimals. The prejudice was in favour of infinitesimals, but rigor won.
2d
comment Let T be the set of positive integers, and let E be the set of positive even integers. Prove that |T| = |E|.
in whatever text you are reading look for similar worked examples. If you find none, use another text.
2d
comment Let T be the set of positive integers, and let E be the set of positive even integers. Prove that |T| = |E|.
don't be so hesitant. Follow the definitions! (and yes, that is what you'd do).
2d
comment Let T be the set of positive integers, and let E be the set of positive even integers. Prove that |T| = |E|.
what can you say about the function $n\mapsto 2n$?
Jul
23
answered Is there a group-theoretic proof of the Riemann rearrangement theorem?
Jul
23
answered Convergence in a metric space
Jul
23
answered If $H$ and $K$ are subgroups of G then $H \times K$ is a subgroup of $G \times G$
Jul
22
awarded  Good Answer
Jul
22
answered Euclidean space and Euclidean geometry
Jul
22
revised Is there a simple way to illustrate that Fermat's Last Theorem is plausible?
added 1 character in body
Jul
22
comment Is there a simple way to illustrate that Fermat's Last Theorem is plausible?
@EricStucky I'm not sure. The Goldbach conjecture is not on the verge of being solved.
Jul
20
comment If $G,H$ are monoids and not groups, prove that $f(e_G)=e_H$ may be wrong.
$2$ is not an element in $\mathbb Z^*_4$.
Jul
20
comment If $G,H$ are monoids and not groups, prove that $f(e_G)=e_H$ may be wrong.
it is a group. Why?
Jul
20
comment If $G,H$ are monoids and not groups, prove that $f(e_G)=e_H$ may be wrong.
the argument you give does not make sense. Why won't you give an example of monoids $G,H$ and a function $f:G\to H$ which preserves the operation, but not the units?
Jul
19
awarded  Enlightened
Jul
19
comment If $f(x)$ is discontinuous at $x=0$, can $\int_{-1}^1 f(x)dx$ exist.
the plural of infimum is infima. For supremum is suprema.
Jul
19
revised What is the intuition and motivation behind a norm on a space?
edited title
Jul
19
revised What is the intuition and motivation behind a norm on a space?
deleted 1 character in body
Jul
18
awarded  Nice Answer
Jul
18
answered If $f(x)$ is discontinuous at $x=0$, can $\int_{-1}^1 f(x)dx$ exist.