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Aug
23
comment Directly prove that $2x^2 -4x + 3 > 0$ for all real $x$
The technique is called completing the square.
Aug
23
comment Can we get just $3$ from $\pi$?
How about $\pi(5)$, where $\pi$ is the prime-counting function?
Aug
23
comment Polydisc is not biholomorphic to any strictly pseudoconvex domain
@Math Make a holomorphic change of coordinates so that $D$ becomes strictly convex near $\phi(0)$, locally given by $y_2<h(x_1,y_1,x_2)$ where $h$ vanishes to second order. Compose $\phi$ with the projection on the second coordinate $z_2$. The result is a one-variable holomorphic map which maps the interior point $0$ to a boundary point of its image, and such a map has to be constant.
Aug
22
revised Polydisc is not biholomorphic to any strictly pseudoconvex domain
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Aug
22
comment History of notation: “!”
@TonyK Cajori agrees with Hilbert that it should be $\underline{\big|n}$. He also says this notation was introduced in 1827, and became somewhat popular only after Todhunter used it in his texts around 1860.
Aug
22
answered Polydisc is not biholomorphic to any strictly pseudoconvex domain
Aug
22
comment Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
@ChristianBlatter I think not, but I see the Cambridge typesetting standard disagrees with me. From this description of the ISO standard, "italic symbols should be used only to denote those mathematical and physical entities different values," and "Any other symbol that was not dealt with in the preceding section must be set in roman font". It is my interpretation that if something cannot assume different values then it is because it is the name of something.
Aug
21
revised Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
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Aug
21
answered Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
Aug
20
awarded  Nice Answer
Aug
20
revised Disproving the claim that the numbers 1+2+4, 1+2+4+8, 1+2+4+8+16… alternate between prime and composite
added 180 characters in body
Aug
20
answered Disproving the claim that the numbers 1+2+4, 1+2+4+8, 1+2+4+8+16… alternate between prime and composite
Aug
20
answered Analysis of a Holomorphic function $f$ given $1 \geq |f '(z)|$.
Aug
20
comment Analysis of a Holomorphic function $f$ given $1 \geq |f '(z)|$.
There is an obvious counterexample: The function $f(z)=z$ satisfies your conditions and is not constant.
Aug
19
comment Mathematical literature to lose yourself in
A related quote by André Weil: "In 1947, in Chicago, I felt bored and depressed, and not knowing what to do, I started reading Gauss's two memoirs on biquadratic residues, which I had never read before (....) This led me in turn to conjectures about varieties over finite fields."
Aug
19
answered Mathematical literature to lose yourself in
Aug
19
answered Spherical geometry as an example of non euclidean geometry
Aug
14
comment Implicit Function Theorem Help in a Macroeconomic Model
The two methods give you the same equations to solve, so in terms of computational difficulty they are fully equivalent. If you prefer, you can solve the first equation for ${\rm d}K$ and substitute into the second. You may also "divide through" by ${\rm d}Y$ to get equations between derivatives instead of differentials.
Aug
13
comment Implicit Function Theorem Help in a Macroeconomic Model
The usual way to think about this is that for each fixed value of $Y$, you can solve your system of equations and find $C$ and $K$. Now what you are supposed to describe in your problem is how your solution of $C$ and $K$ changes when you start with a slightly different value of $Y$.
Aug
13
answered Implicit Function Theorem Help in a Macroeconomic Model