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location Fiji
age 37
visits member for 2 years, 5 months
seen 6 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.


Oct
19
comment Continuity and Boundedness on R imply uniform continuity?
is this homework?
Oct
19
comment What is so special about Klein 4-group?
what do you mean by "category of its own"? It's just the name of this group. It's the smallest non-cyclic group, which is about the only interesting thing one can say about it.
Oct
19
answered Understanding homomorphism and kernels
Oct
19
comment How to formalize proofs
I did say "clear the denominators", right?
Oct
18
answered How to formalize proofs
Oct
18
comment Functoriality of fundamental group
what is $\pi_1(X)$ if you did not specify a base-point?
Oct
18
comment Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?
No, no such number exists.
Oct
18
comment Yoneda Lemma: definition of Yoneda functors
just try to define what the functor does to a function $f:S\to T$ and see what happens.
Oct
18
comment Systematic way to represent any irrational number
If you are trying to systematically enumerate the reals, then of course this can't be done since no enumeration exists at all. What then do you mean by "systematically representing the reals"?
Oct
18
comment Find all almost lower bounds and almost upper bounds of $\{\frac 1n: n\in \Bbb N\}$
Imagine that $\alpha = 1/2$ and now think again about what you just said.
Oct
17
answered Find all almost lower bounds and almost upper bounds of $\{\frac 1n: n\in \Bbb N\}$
Oct
17
comment Find the next number
en.wikipedia.org/wiki/Look-and-say_sequence
Oct
17
comment Koch snowflake versus $\pi=4$
and (+1) for introducing arc length into the picture.
Oct
17
comment Koch snowflake versus $\pi=4$
my apologies @HansLundmark, you are correct. I took rectifiable to mean "having finite Euclidean metric", i.e,. s.t. the usual integral formula for the length is finite. Of course the Koch snowflake has non-differentiable perimeter, so this does not apply. Buy you are right, since rectifiable is a bit more general than that.
Oct
17
comment Koch snowflake versus $\pi=4$
@HansLundmark, not quite. This argument actually shows nothing.
Oct
17
comment Koch snowflake versus $\pi=4$
The perimeter of the Koch snowflake is not a 1 dimensional curve. In particular, it need not have a Euclidean length. So, the claim that the perimeter is $\infty $ by this method is wrong. For its fractal dimension perhaps it has a suitable measure, which may be infinity, I don't know.
Oct
17
comment Koch snowflake versus $\pi=4$
which source claims the perimeter of the Kock snowflake is $\infty$?
Oct
17
comment Is there a quotient map between arbitrary topological spaces?
Still obviously not. Cardinality of the underlying sets is not enough as there is also an obvious cardinality relation between the topologies themselves.
Oct
17
comment Is there a quotient map between arbitrary topological spaces?
Of course not. The quotient is surjective, so if $|X|<|Y|$, then no quotient mapping $X\to Y$ can exist. If you refine your question somewhat perhaps a more interesting answer will emerge.
Oct
17
comment Is the theory of dual numbers strong enough to develop real analysis, and does it resemble Newton's historical method for doing calculus?
@isomorphismes the orders of magnitude here refer to infinitesimals being an order of magnitude below the positives reals. In this context .001 and .000000000000001 have the same order of magnitude.