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2m
answered Notation problem in integration
19h
awarded  Nice Answer
22h
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
23h
answered Disproving the claim that the numbers 1+2+4, 1+2+4+8, 1+2+4+8+16… alternate between prime and composite
1d
answered Analysis of a Holomorphic function $f$ given $1 \geq |f '(z)|$.
1d
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.
2d
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."
2d
answered Mathematical literature to lose yourself in
2d
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
Aug
13
comment Implicit Function Theorem Help in a Macroeconomic Model
What do you know about the function $f$?
Aug
12
comment Economic Applications of Game Theory
A loss of $P$ is the same as a gain of $-P$.
Aug
12
comment Economic Applications of Game Theory
I did not downvote, but have you copied the solution faithfully? The right hand side should be $u(0)$ instead of $P(0)$, and $x$ does not have the same meaning in the problem and in the solution.
Aug
12
answered Economic Applications of Game Theory
Aug
12
comment Economic Applications of Game Theory
Don't use the same letter $P$ with two different meanings! In your formula, $P$ is used both for the price that the investor is willing to pay and for the probability that the homeowner goes bankrupt.
Aug
10
revised What is the area of the parking lot?
rolled back to a previous revision
Aug
7
comment What meaning did Riemann assign to $dx$?
Michael Spivak has a long chapter on Riemann's paper in Volume 2 of his Comprehensive Introduction to Differential Geometry.
Aug
7
comment The fastest way to count prime number that smaller or equal N
Have you tried the sieve of Erathostenes?