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  • 31 votes cast
Jan
28
comment Why does $\exists x\,\ x = x$?
@AsafKaragila thanks for the links. I'd argue that this isn't a duplicate however. I see how the existence of the empty set follows from the existence of a set, but my question isn't about the former.
Jan
28
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 $\forall x\,\ x = x$.
Jan
28
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 $\exists x\,\ x=x$.
Jan
28
asked Why does $\exists x\,\ x = x$?
Aug
30
awarded  Popular Question
Aug
22
awarded  Yearling
Aug
8
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.
Jul
25
awarded  Nice Question
Mar
2
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?
Dec
4
accepted How did people calculate numerical values of transcendental and trigonometric functions?
Dec
4
revised How did people calculate numerical values of transcendental and trigonometric functions?
edited title
Dec
4
asked How did people calculate numerical values of transcendental and trigonometric functions?
Nov
29
answered vector subspaces in $\mathbb{R}^{4}$
Nov
28
suggested rejected edit on Showing $f(0) = 0$ and $|f'(x)| \leq M$ implies $|f(x)| \leq M |x|$.
Oct
29
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.
Oct
29
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?
Oct
27
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?
Oct
26
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.
Oct
9
answered How do i differentiate this function with e to the x and fraction?
Oct
8
comment How do i differentiate this function with e to the x and fraction?
Is this homework?