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


1d
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?
1d
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.
1d
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.
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
comment Is a nonzero number infinitely greater than zero?
what is your question?
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
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
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
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.
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
that is true only if $a\ne 0$. But $0/0=1$ is not inconsistent with the equalities you had written.
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
$0/0=1$ is consistent with the equalities you write. Moreover, it is incorrect to think of L'Hopital's rule as "dividing by a quantity that approaches zero. In fact, there is no such thing as "a quantity that approaces zero". Limits are numbers, not approximations or anything vague such as quantities approaching anything.
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
I think the title of the questions clarifies OP's intentions sufficiently well, though the question certainly could have been worded with more care. However, saying it's undefined cause it's undefined is a poor argument if it's an argument at all.
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
exactly. The argument for why $a/0$ for $a\ne 0$ is not definable is different than why $0/0$ is not definable.
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
OP was asking why $0/0$ can't be defined. The whole question is "how do you know you can't meaningfully define $0/0$?"
Nov
17
comment Seeking elegant proof why 0 divided by 0 does not equal 1
@BenjaminAlderson, your objection is not valid. The reason $0/0$ is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals. It is perfectly reasonable to contemplate particular vales for $0/0$ and obtain a contradiction. This is how we know it is impossible to define it in any reasonable way. To say, it's simply undefined so this is invalid is not the way mathematics is done. OP is interested in why it can't be defined, not in blindly accepting authority.
Nov
17
comment Question on Uniform Continuous Functions
not quite. To use the definition, start out with what it means for 1/f to be uniformly continuous. I.e., let $\varepsilon >0$. We are looking for blah blah blah.... Now, the epsilon is given. Find its $\delta$ (using $k$ somehow).
Nov
15
comment “Too many” vectors are linearly dependent—can it be generalized to infinite-dimensional spaces?
no, the union of independent sets need not be independent.
Nov
14
comment Finding limit without using L'Hopital rule
how about you do your own homework?