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448107
bio website sites.google.com/site/…
location Fiji
age 37
visits member for 2 years, 3 months
seen 4 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.


7h
comment Are $+\infty$ & $-\infty $ elements of the real number line?
no, they are not real numbers.
2d
comment The category with binary relations as objects
if it works for any category, why should it not work for Rel???
2d
comment The category with binary relations as objects
to second @Hurkyl 's comment: For any category you can construct the category of arrows of it. The objects are the morphisms and the morphisms are pairs of morphisms as making a commutative square as you describe. This works for Rel as well.
2d
comment What is the average of no numbers?
Your objection is a weak one @Mehrdad. It is perfectly ok to translate things and get the same thing back. For instance, translating any set of reals by $0$ results in the same set. Translating $\mathbb R$ by any number results in the same set again. Translating $\mathbb Z$ by any integer yields $\mathbb Z$ again. Similarly for $\mathbb Q$. Your objection seems to stem from an expectation of yours (and I stress, it is yours) that translation should always produce something different than what you started with. This is simply not the case.
Aug
27
comment What is the average of no numbers?
Let us continue this discussion in chat.
Aug
27
comment What is the average of no numbers?
no, "it" is the mean, not the set. It was about one-trillion percent rigorous. I suggest taking it to a chat btw.
Aug
27
comment What is the average of no numbers?
@Mehrdad you need to understand the difference between: "translate the set first, then take the mean", and "first take the mean, then translate it". The mean has the property that these operations yield the same result. What the second paragraph does is conclude no assignment of the mean to the empty set still has this property and uses it as a reason against assigning any value to the mean of empty mean. This is standard extrapolation from general properties to extreme cases.
Aug
27
comment What is the average of no numbers?
@Mehrdad I know. You can still translate them. Just like you can take the empty sum, empty product, empty infimum, empty supremum. You can translate the empty set, you can scale it. It's just a set.
Aug
27
comment What is the average of no numbers?
@Mehrdad every member of the set of which I take the mean.
Aug
27
comment What is the average of no numbers?
@Mehrdad yes, the empty set does not change upon a translation. But the mean does translate with a translation, and thus one can't associate a translation consistent value for the mean of the empty set. That is what the second paragraph is saying and I'd appreciate it if you say what is wrong with that.
Aug
26
comment Is there such a classification as Co-Paradox?
@MaliceVidrine I meant that naively (and Russell's paradox is a paradox of naive set theory) the question whether the Russell sets belongs to itself or not is unresolved. I did not mean that the paradox is unresolved as clearly any axiomatization of set theory proves that if a model exists, then the Russell "set" does not exist.
Aug
26
comment Is there such a classification as Co-Paradox?
I'm sorry, but I think we are having a mis-communication here. I'll just say then that the way we use the term universe is meant to talk about all sets or elements of interest to a particular situation. Not that there is a universe which contains all sets in a particular model of set theory. Moreover, there is a well-developed theory of Grothendieck universes. I don't think though OP was asking about any of that.
Aug
26
comment Is there such a classification as Co-Paradox?
nice variation!
Aug
26
comment How to make the Symmetric Distance a metric?
Your question is starting to get a bit chaotic, you may wish to spend some time thinking about what you want to do. In any case, if you take your sets to be closed then they are measurable but the area of the symmetric difference will not give you a metric. you may wish to read about the Hausdorff metric.
Aug
26
comment How to make the Symmetric Distance a metric?
How do you know the symmetric difference has any area at all? you need measurable sets to make this work so you need to refine your definition of $S$.
Aug
26
comment How to make the Symmetric Distance a metric?
nope, it does not. To be a metric you need to assign a non-negative real number to any two elements. The symmetric difference is a set, not a number.
Aug
25
comment If $G/K\cong H/K$ must $G\cong H$?
You are welcome and no, not in any profitable way.
Aug
24
comment Uniqueness of the direct product decomposition of finite groups
@Timbuc you are right. I was sure OP was talking about abelian groups.
Aug
24
comment Why do we study representations of groups but not fields?
@MarcvanLeeuwen Yes! The thing is to have a useful representation theory and that usually comes from considering particularly nice (i.e., geometrically rich) structures). Of course, any group can be represented as a group of permutations on a set, but a set is not terribly rich. Similarly for representations of rings, as you say, just having an abelian group does not yield terribly interesting stuff. Having a vector space there helps.
Aug
24
comment Definition of characteristic polynomial
you need to argue that matrices related by change of base have the same determinant, otherwise what you defined above may be basis dependent. Besides, I don't think this is what OP asked.