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Jul
30
comment How many sides does a circle have?
Of course the proper answer would have been $\mathfrak c$ ;-)
Jul
30
revised $\nabla \cdot \color{green}{(\mathbf{F} {\times} \mathbf{G})} $ with Einstein Summation Notation [Stewart P1068 16.5.27]
Replaced non-formula LaTeX by proper Markdown
Jul
30
comment What does limit actually mean?
Sorry, I can't go to chat from here (a technical problem); so that will have to wait until I'm at home (in at latest two hours).
Jul
30
comment What does limit actually mean?
Continuous or not defined.
Jul
30
comment What does limit actually mean?
If $g$ were not defined at $x=1$, then the limit would certainly exist. But the point is that you $did$ define $g$ at point $x=1$. Now with the definition you gave (with $0<$) the limit indeed exists, but with the definition I know it wouldn't. Note that the limit would also exist if $g(x)$ were undefined for all points in $\{1+1/n: n\in \mathbb N\}$, despite the fact that your definition doesn't exclude those points. This is because the condition of course has to be fulfilled only in the domain of $g$ (while the limit is defined on the closure of the domain).
Jul
30
revised What does limit actually mean?
added 1 characters in body
Jul
30
comment What does limit actually mean?
The $\epsilon$-$\delta$ limit definition I know does not have the $0<$ part. Especially, the limit $\lim_{x\to 1}g(x)$ does not exist for the definition I know. (BTW, even with your definition it would be $2$, not $8$.)
Jul
30
revised How is the property called that makes $(a\cdot b)/c = (a/c)\cdot b = a\cdot (b/c)$
added 25 characters in body; edited title
Jul
30
comment How to prove a claim stating that there are lots of real numbers which are not rational.
How do you do a constructive proof that something does not exist?
Jul
30
comment Does weight equate volume or surface area?
I think that's more of a physics than a mathematics question. Anyway, you can try it out: Take something you can easily weight and divide (say, a piece of butter), weight it, cut it in half (thus increasing the surface, but not the volume), and weight the two halves together.
Jul
29
answered Coordinates (in vectors space and on manifold)
Jul
29
revised Why does $16^0 = 1$ and not $0$
added 274 characters in body
Jul
29
answered Why does $16^0 = 1$ and not $0$
Jul
26
comment Can you provide me historical examples of pure mathematics becoming “useful”?
@AD: I'd say people accept real numbers because those can be used for things we routinely do with numbers: Specify lengths, angles, ratios of quantities ... however everything we measure is inherently found to be real (this is even true in quantum mechanics: measurement results are eigenvalues of hermitean operators, hence real). You can point to a square and speak about the length of the diagonal. You can point to a circle and can talk about the circumference. However there's nothing you can point to where you immediately see "oh right, that one has the value i".
Jul
24
comment Division is equal to zero
Actually, the denominator does enter into finding the roots: After you've found the roots of the numerator, you have to check that they are not roots of the denominator.
Jul
24
comment Number of ways of partitioning a number $n$ in unique ways.
If it's getting slow, it may mean that you repeatedly calculate the same partition. Make sure that you store any results you already calculated and don't calculate them again.
Jul
24
comment What does this series converge to?
Which series? As is, you've got a finite sum. Do you mean $\lim_{n\to\infty}$ of that sum? Also, is $S=\sum_{i=1}^n s_i$ or $S=\sum_{i=1}^\infty s_i$?
Jul
24
revised What does this series converge to?
edited title
Jul
23
comment Subtraction for linear space.
Maybe one way to define a "subtraction" (scare quotes, because it is not a subtraction in the ordinary sense) could be $V_1-V_2:=V_1\cap V_2^\bot$ where $V_2^\bot$ is the orthogonal subspace to $V_2$, that is, the set of vectors orthogonal to all vectors of $V_2$. Of course that's only defined in inner product spaces. But then, assuming the standard inner product, indeed for your $V_1$ and $V_2$, $V_1-V_2$ is spanned by $\{e_3\}$.
Jul
23
comment Reproduction, Probability, and Independence
@tomasz: I of course meant a polygamist family. But then, why should a two-men-three-women family not be possible as well? :-) But I wonder about those tree women you speak about, are they maybe Ents? ;-)