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 Jan28 comment Why does $\exists x\,\ x = x$? @CliveNewstead I would agree that this would be true if I accept the empty set axiom, but I thought the point was that we didn't need one. Without it, $\exists x\,\ x = x$ wouldn't follow from the axiom $\forall x\,\ x = x$. Jan28 comment Why does $\exists x\,\ x = x$? @CliveNewstead I don't see why "there exists a set $x$" is meaningless, but, even supposing it is, I still don't see why I can accept $\exists x\,\ x=x$. Jan28 asked Why does $\exists x\,\ x = x$? Aug30 awarded Popular Question Aug22 awarded Yearling Aug8 comment Is the vector cross product only defined for 3D? I don't understand why we have to prove that a cross product exists for any given $d > r$ - for any set of vectors with size $r$, any matrix which has a column space defined by the basis of this set of vectors is guaranteed to have a rank of at most $r$, and so a null space of $d-r > 0$. Since this null space is always nontrivial, a vector satisfying the criteria for the cross product can always be found. Jul25 awarded Nice Question Mar2 answered Is the equality $\frac{d}{dk}\int_{-k}^k \sqrt{f_0(y)f_1(y)}\,\mathrm{d}y=\sqrt{f_0(k)f_1(k)}-\sqrt{f_0(-k)f_1(-k)}$ correct? Dec4 accepted How did people calculate numerical values of transcendental and trigonometric functions? Dec4 revised How did people calculate numerical values of transcendental and trigonometric functions? edited title Dec4 asked How did people calculate numerical values of transcendental and trigonometric functions? Nov29 answered vector subspaces in $\mathbb{R}^{4}$ Nov28 suggested rejected edit on Showing $f(0) = 0$ and $|f'(x)| \leq M$ implies $|f(x)| \leq M |x|$. Oct29 comment Show that the function $g(x)=x^4+x^3+1$ is one-to-one on $[0,2]$ Oh, sorry, never mind. For some reason I interpreted "factor" as "divide out by." My mistake. Oct29 comment Show that the function $g(x)=x^4+x^3+1$ is one-to-one on $[0,2]$ Why are you allowed to factor out $x_1-x_2$ if they're equal? Oct27 comment Can you approximate a vector field? It would be one half, because there is an overlap in the information being used for the averages. But the actual implementation of averaging the is immaterial - you could think of lots of ways to do so. Yes, I was referring to a discrete grid of vectors that represents the vector field - that was what your question was asking - how to show general trends - no? Oct26 comment Can you approximate a vector field? Yes - there would be less information about the field in the image. For example, if you plot some vector field $\vec v$ on a grid with steps $\Delta y$ and $\Delta x$, then after averaging $\vec v'(x, y) = (v(x, y) + v(x+\Delta x, y) + v(x, y+ \Delta y) + v(x-\Delta x, y) + v(x, y- \Delta y))/5$ and plotting a vector on every point on the grid with steps $2\Delta y$ and $2\Delta x$, you'll end up with half the vectors you started with. Oct9 answered How do i differentiate this function with e to the x and fraction? Oct8 comment How do i differentiate this function with e to the x and fraction? Is this homework? Aug28 comment Calculate the area on a sphere of the intersection of two spherical caps Ah, I understand now.