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7h
comment On dimension of algebraic sets
Note that $\pi(\bigcup V_i) = \bigcup \pi(V_i)$. Can you apply the closure operator to both sides?
9h
comment F is a vector space and U, V, and W are subspaces of F. Prove that $U\bigcup V\bigcup W$ is a subspace of F if and only if $U,V\subset W $.
In addition to the other mistakes in the statement already pointed out, there's a more subtle mistake, in that the statement is false when the base field is $\Bbb F_2$: Take $F$ to be a $2$-dimensional vector space over $\Bbb F_2$, and take $U,V,W$ to be the $1$-dimensional subspaces. (One can direct-product this example up to make higher-dimensional examples.)
9h
comment Irrational roots conjugate theorem
It's tough to know what to concentrate on when you ask multiple questions in the same post. I wanted to make sure you knew that your first mathematical assertion is incorrect (or at least not stated as you wanted to state it). As for your second question, you say "how can we use the theorem in the first place" ... what "theorem" are you referring to?
1d
comment Irrational roots conjugate theorem
Regarding the cubic: $x(x-1)(x-\sqrt2)$ is a counterexample. And it doesn't seem like you meant to specify that the cubic has rational coefficients, for it's impossible for a polynomial with rational coefficients to have exactly one irrational root.
1d
answered Intersection of dense sets in $\mathbb{N}$
2d
comment Separation and Russell's paradox
Note the commands $\exists$ (backslash exists) and $\forall$ (backslash forall), which will make your question much easier to read.
2d
comment Prove that the set $U = \{(123), (124), … , (12n)\}$ can be used to generate $A_n$.
So far you've only talked about $3$-cycles; $A_n$ contains many more types of elements than that.
2d
comment Sum of Complex Numbers and Modulus Inequality
Startning hint: of the four quadrants defined by the real and imaginary axes, one of them must contain at least $n/4$ of the numbers $z_j$.
Feb
5
comment Transforming parts of functions
They are plentiful. $f(t) = t$ for $t\le 3$, $f(t) = (t+3)/2$ for $t\ge3$ is such an example.
Feb
5
comment Homogeneous space minus a point
If you allow non-connected homogeneous spaces, the answer seems to be no: let $X$ be the disjoint union of two circles, for example.
Feb
5
comment Transforming parts of functions
Replace $t$ by a function that's roughly linear for $t<3$ but increases more slowly for $t>3$.
Feb
5
answered A question in limit matrix polynomial
Feb
3
answered Asymptotic bounds on sum of primes
Feb
3
comment On finding the volume using triple integral
seems right to me!
Feb
2
comment The minimum of two big-O functions
I think the second option is clearer than the first, and quite reasonable. You might possibly write $\alpha(1-O(\min\{k,m\}/n)) \le \chi(G_N) \le \alpha$ as well.
Feb
1
comment What lies beyond the Möbius transform?
Perhaps that information would be a helpful addition to the problem statement itself.
Feb
1
comment What lies beyond the Möbius transform?
Why do you think there should be an analogue? Why should there even be an interpretation of a single $3\times3$ matrix in trems of functions on the complex plane?
Feb
1
comment Does $\lim_{x \to 1^-} \sum_{n=0}^\infty x^{n!} = \infty$?
The fact that $$\lim_{r\to1^-} \sum_{n=0}^\infty r^{n!} = \sum_{n=0}^\infty \lim_{r\to1^-} r^{n!}$$ follows from the fact that all the summands are nonnegative (Tonelli's theorem).
Jan
31
comment Linear equations and the gcd
I don't think you're reading your source correctly. One can't prove that an equation has solutions by assuming the existence of two solutions. Perhaps you're reading a proof of the characterization of all solutions? I also don't know what you mean by "$x_2$ and $y_2$ are both contained in $k$", since $k$ is a number.
Jan
31
comment Behavior of limits when exponent approaches $-\infty$
What does $\lim\limits_{\mu\to 0^+} q_\mu = e^{q_\mu} e^{-\varepsilon}$ mean? The answer can't have a $\mu$ in it (not can $\varepsilon$ tend to $0$ with $\mu$) if the limit is being taken over $\mu$.