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18h
comment Intersections of connected components of real curves
In can happen in the $d=2$ case : pick $3$ points on the same branch of a hyperbola, and draw their circumscribed circle. (though the branches are connected through $\Bbb P^2(\Bbb R)$ so idk if that counts)
1d
answered Find a Mobius Transformation that carries the points $ -1, i, 1+i$ to the following:
1d
comment Exact Expression for numerical Solution 0.9595767
yeah those three algebraic equations give out a polynomial in $a$ of degree $6$.
2d
comment Find a Mobius Transformation that carries the points $ -1, i, 1+i$ to the following:
@Alex M the source of the problem is that he is assuming that $a,b,c,d$ are real. Since the transformation is homogeneous in $a,b,c,d$, you can multiply everyone by a scalar and not change the transformation, so you don't lose anything by assuming the numerator is $z+1$ instead of $c(z+1)$ for nonzero $c$. It is a perfectly legit thing to do here.
2d
comment Function $\Bbb Q\rightarrow\Bbb Q$ with everywhere irrational derivative
oh i see, what is not clear is that the minimum of the parabola doesn't dip super low below $(r_n,y_n)$ ?
2d
comment Function $\Bbb Q\rightarrow\Bbb Q$ with everywhere irrational derivative
give large positive leading coefficients to all the upper parabolas and large negative (like -10^100 if that's not clear) leading coefficients to all the lower parabolas. Think about the parabolas geometrically. The larger the leading coefficient of the upper parabola is, the thinner it is and the faster it tries to escape to infinity (crossing the upper border) and eventually it won't touch the lower border.
2d
answered Function $\Bbb Q\rightarrow\Bbb Q$ with everywhere irrational derivative
2d
comment If there is a branch of $\sqrt{z}$ on an open set $U$ with $0 \notin U,$ then there is also a branch of $arg$ $z.$
I swear this is a duplicate
2d
comment Function $\Bbb Q\rightarrow\Bbb Q$ with everywhere irrational derivative
yes, there are lots of them, you can use a just-do-it proof gowers.wordpress.com/2008/08/16/just-do-it-proofs
Feb
9
awarded  Enlightened
Feb
9
awarded  Nice Answer
Feb
7
comment The set of polynomials which “cut out” smooth subsets of projective space is open and dense
what's a smooth subset of $\Bbb P^n$ ?
Feb
7
answered Can a complex argument into this function ever yield a real result?
Feb
7
comment all but one sub-strings within a cyclic string
It is always possible to build one. For example with $q=n=2$ you can get "001", it avoids "11" but it has "00" "01" and "10".
Feb
4
revised How to simplify $\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}$
added 7 characters in body
Feb
4
comment Variety of proofs of a simple proposition in arithmetic
I really don't see how we can go about this without recognising the multiplicative structure of $B$ (of your sequence $(a_n)$), and of the scaling process. But then, when we have them it becomes easy and there are several ways to narrate it. For example one can use that $B$ is stable by products and lcms to easily get that you can't pick up someone twice.
Feb
4
revised How to simplify $\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}$
added 288 characters in body
Feb
4
answered How to simplify $\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}$
Feb
1
comment Wanted: Polynomial $P(x)$ with $P(-l(l+1))=1/(2l+1)$, for $l\in \mathbb{N}$
so are you asking if the sequence for each coefficient is convergent, and if so, to what ?
Feb
1
revised Erasing numbers from the front of the row
added 2 characters in body