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Jul
8
comment Proof by Cases: $\operatorname{max}\{x,y\} + \operatorname{min}\{x,y\}=x+y$
@Trancot: I guess what you should learn from that is that sometimes the best way to prove a general relation is to divide the problem into a complete set of special cases which are easier to treat individually.
Jul
8
answered How does knowing a function as even or odd help in integration ??
Jul
8
revised $\nabla \cdot \color{green}{(\mathbf{F} {\times} \mathbf{G})} $ with Einstein Summation Notation [Stewart P1068 16.5.27]
added 143 characters in body
Jul
8
answered $\nabla \cdot \color{green}{(\mathbf{F} {\times} \mathbf{G})} $ with Einstein Summation Notation [Stewart P1068 16.5.27]
Jul
8
comment Is there a standard name for the relation $X \times Y$?
I think "full relation" is best, because it has a natural counterpart in "empty relation". While "maximal relation" has also a natural counterpart "minimal relation", the latter might be interpreted as relation where there's exactly one pair of related elements (because otherwise all elements are unrelated). "Top" also has a natural counterpart "bottom", but the meaning is not as obvious (what does it mean for a relation to be higher than another one?). "total" and "complete" don't have natural counterparts, as far as I can see.
Jul
7
comment Which function is appropriate for the geometrical shape mostly used as LOVE symbol
Related: math.stackexchange.com/q/12098/34930
Jul
7
answered Why does the Dedekind Cut work well enough to define the Reals?
Jul
7
awarded  Nice Question
Jul
6
comment When is a metric space Euclidean, without referring to $\mathbb R^n$?
Ah, I've now seen the $n=2$ counterexample for corollary 2.3 in the article; that one would violate my (U) condition, e.g. for $A=(-1,0), B=(0,0), C=(1,0), D=(0,1)$. I wonder if there exist counterexamples which don't violate (U).
Jul
6
comment When is a metric space Euclidean, without referring to $\mathbb R^n$?
@BrianRushton: Thanks, that's a very interesting read. I wonder if it would be possible to replace the euclidean four point property by some "tetrahedron inequality" (or inequalities). OTOH the need for this four-point property makes me suspect that my conditions may not be sufficient, because it shows that for dimension $3$ there obviously are additional freedoms which I've not explicitly taken into account. I wonder what a convex metric space without the euclidean four point property would look like.
Jul
6
comment Show that$ f(x)=x^5-3$ is solvable by radicals over $\mathbb{Q}$.
What about inserting $3^{1/5}$ and observing that you get $0$?
Jul
6
revised Why don't we define division by zero as an arbritrary constant such as $j$?
added the name of the structure
Jul
6
comment Why don't we define division by zero as an arbritrary constant such as $j$?
@FlybyNight: See the second link in my answer. I've now added the explicit name in the text.
Jul
6
comment When is a metric space Euclidean, without referring to $\mathbb R^n$?
@BrianRushton: Your link is to a Google search. Which of the many links (which almost certainly show up in different order for me than for you) is the one you're talking about?
Jul
6
comment Why don't we define division by zero as an arbritrary constant such as $j$?
Actually, even $0/0$ is defined in wheels.
Jul
6
answered Why don't we define division by zero as an arbritrary constant such as $j$?
Jul
6
comment When is a metric space Euclidean, without referring to $\mathbb R^n$?
@CameronWilliams: There are surely many different ways to define Euclidean spaces. However I'm specifically interested to do it from the metric.
Jul
6
comment When is a metric space Euclidean, without referring to $\mathbb R^n$?
@CameronWilliams: So how do you define "all norms" if all you have is a set $M$ and a single(!) function $d\colon M\times M\to M$?
Jul
6
comment When is a metric space Euclidean, without referring to $\mathbb R^n$?
@ClementC.: Strange, now your first link works. Must have been a temporary server problem. Anyway, even your second link is not what I want because it also refers to an additional structure, namely the Euclidean vector space defined in your first link.
Jul
6
comment When is a metric space Euclidean, without referring to $\mathbb R^n$?
@ChrisEagle: OK, now corrected. Thank you.