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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.


Dec
28
answered Can we teach calculus without reals?
Dec
28
comment What is the difference between a cover and a subset?
you are thus asking what is the difference between a set containing $X$ and a collection of sets that together (i.e., their union) contain $X$. Well, clearly, every set containing $X$ is also a cover of $X$, but not vise versa. E.g., $\{x\}_{x\in X}$ is a cover of $X$.
Dec
27
comment Do we really need reals?
In a nutshell, perhaps. Perhaps it is not a wise thing to put the reals in a nutshell.
Dec
27
revised Do we really need reals?
added 7 characters in body
Dec
26
answered Proving infinite order.
Dec
25
comment Do we really need reals?
but if all you have access to are rational multiple of, say, $\pi$, does it matter at all that $\pi$ is transcendental? What if I decided to rescale the outcomes to be rational multiples of a biniguksu, are my outcomes in any way a biniguksu? what the hack is a biniguksu??? (well, it does not matter cause all I have is rational multiples of it, so it's is all just isomorphic to the rationals).
Dec
25
comment Do we really need reals?
I must disagree @Hurkyl all measurement outcomes are rational. What you show above is that you can change the scale (to $\pi$ or introduce complex numbers), or perform some further computation on your rational outcome. It does not change the fact that the outcome you got was rational.
Dec
25
awarded  Good Answer
Dec
24
comment Brouwer theorem
what is this '+' space exactly?
Dec
24
comment To show that $f (x) = | \cos x | + |\sin x |$ is not one one and onto and not differentiable
thanks again @coffeemath
Dec
24
comment To show that $f (x) = | \cos x | + |\sin x |$ is not one one and onto and not differentiable
slip of the copy paste... thanks @coffeemath
Dec
24
revised To show that $f (x) = | \cos x | + |\sin x |$ is not one one and onto and not differentiable
edited body
Dec
24
answered To show that $f (x) = | \cos x | + |\sin x |$ is not one one and onto and not differentiable
Dec
24
awarded  Nice Answer
Dec
23
comment Do we really need reals?
I think we are saying the same thing. Which physicist will look at the reading off a device, something like 0.5434466, and say "that's irrational"? What you read off a device is a rational approximation to the actual outcome (which is often irrational). This is exactly what @SeanD is saying and what I tried to say in my answer.
Dec
23
awarded  Nice Answer
Dec
23
answered Easy example why complex numbers are cool
Dec
23
revised $infA\leq SupA$
deleted 2 characters in body
Dec
23
answered Do we really need reals?
Dec
23
comment What is a “category”?
and the morphisms can be composed when their domain and codomain match, and the composition is associative, and there are identity morphisms which behave like identities for the composition (and morphisms don't need to be functions at all).