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1d
answered Why count it this way?
1d
comment Approximate theorems
Suppose in a specific engineering application I need e.g. a certain function $f(x)$ to be $0$ for all $x$ in the interval $[0, 100]$. If I happen to have a proof that $f(x) = 0$ for all $x$ in $[0,\infty)$ then I can use that. If I don't, but I can prove that $f(x) = 0$ for all $x$ in $[0, 100]$, then that's enough for the purposes of the application. A "counterexample" with $x > 100$ would not be relevant. It's not a matter of "assume the result is true", it's "prove a weaker result".
1d
comment How do i show stability of fixed points of this two.dimensioanl system:$f(x,y)=(y,y²−x²)$?
Yes, use linearization, and no, it's very easy.
1d
answered Does there exist a subsequence whose intersection has measure greater than $1/2$?
1d
comment Approximate theorems
In mathematics we want to know whether a statement is true or false. There's no "for all uses ... we may assume it is true".
1d
answered How do i show stability of fixed points of this two.dimensioanl system:$f(x,y)=(y,y²−x²)$?
1d
answered How close should be the boundary value of $x$ and $y$ to ensure that $|x(t)-y(t)|<0.1$
1d
answered The distribution of the product of Gaussian variable and Rademacher variable.
1d
comment Infinity xkcd style: can a turing machine exist?
Unless your "infinite time" corresponds to a different ordinal...
2d
answered Polynomial function residues
2d
answered Solving a system of non-linear equations
2d
answered How to prove that a Banach space of analytic functions containing $H^\infty$ except the origin is simply connected?
2d
comment At least $500$ of the $25,000$ students in a school come from the same state
If each state had fewer than $500$ students, you'd be able to fit all its students into the boxes, one student per box. But there are only ... boxes in all ...
2d
comment At least $500$ of the $25,000$ students in a school come from the same state
Students are objects. Each state has $499$ boxes.
2d
answered solution of an algebraic equation?
2d
comment Proving existence and uniqueness of a matrix,
Instead of the positive $k$'th root, use ...
2d
answered Excel's EXP function compared to a series expansion
2d
comment German Tank Problem, Confidence Level
OK, you could try $c = 1$ as well. But $1 - 1/1^{10} = 0$, so that won't be the answer. You want $P(M \ge n/c)$ to be at least $9/10$.
2d
comment How do I prove that $ax+by+cz=d$ has infinitely many solutions on $S^2$?
And please: there's a world of difference between "an infinite solution" and "infinitely many solutions".
2d
comment How do I prove that $ax+by+cz=d$ has infinitely many solutions on $S^2$?
Hint: $(x,y,z) = s (a,b,c) + \bf v$ where ${\bf v} \cdot (a,b,c) = 0$, ...