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9h
comment First isomorphism theorem application
1. Yes, your interpretation is correct. 2. One of the isomorphism theorems states exactly $HN/N\cong H/H\cap N$ for general subgroup $H$ and normal subgroup $N$.
2d
comment What is a “lattice” in set theory???
The additional restriction is that meet and join are required for any two elements,
2d
answered What is a “lattice” in set theory???
Feb
5
answered Product of two primitive roots $\bmod p$ cannot be a primitive root.
Feb
5
comment Equality between 3 sets using 3 inclusions
Well, $A\supset B\supset C\supset A$ is the other way with three inclusions. Less would not suffice.
Feb
4
comment Prove a function is in Big-Oh and not in Big-Omega
Well... In this exercise we don't need to find the optimum of $c$ (and $n_0$). The task is to show a $c$ and an $n_0$ such that..... Now here you are $c=26$, $n_0=0$ and the proof that it satisfies the condition.
Feb
4
comment Prove a function is in Big-Oh and not in Big-Omega
The change you probably have in mind would be denoted by an = sign. Here we used $\le$. Well, that's an estimating.
Feb
4
comment Prove a function is in Big-Oh and not in Big-Omega
That's a lazy but clear way for the proof. We used $n,\,n^2\le n^3$. That holds, doesn't it? So choose $n_0=0$ and $c=26$ and that proves. (Actually, we also have $6n^2+20n\in o(n^3)$ where this cheap trick won't solve it..)
Feb
4
revised Prove a function is in Big-Oh and not in Big-Omega
added 28 characters in body
Feb
4
answered Prove a function is in Big-Oh and not in Big-Omega
Feb
3
answered A Subspace of the Degree $3$ Polynomials Space for which $P(5)=0$
Jan
31
comment Find the Primitive of Complex function
Well.. no doubt.. But no closed formula can be given.
Jan
27
answered Why is the definition of subfunctor well-defined?
Jan
27
comment Given a set of (0,1)-vectors, find a subset which adds to the zero vector mod 2
I'm not sure I understand the question. If you have a set of $(0,1)$-vectors, just add them, and it results in a single vector which sums them all altogether the zero vector.
Jan
21
comment Q: Hoffman Linear Algebra question 11 pg. 243, Elementary Canonical Forms
This is just the exercise you should go through on your own. $2\times 2$ matrices are friendly small, characteristic polynomials are quadratic, determinant is easily calculated ($ad-bc$). So that it could help you clear up these notions..
Jan
21
comment How does any map have a “pseudosection” (assuming axiom of choice)?
This exercise is explicitly meant for the category ${\bf Set}$, isn't it? Then we can freely use the things inside this category (points of sets and functions).
Jan
19
comment Closure of set $\{1/n:n\in\mathbb{N}\}$
The interior always exists, and now it is the empty set.
Jan
19
comment Determine the degree of the extension $\mathbb{Q}(\sqrt{3 + 2\sqrt{2}})$.
You can read this last formula as: $\sqrt{3+2\sqrt2}=1+\sqrt2$, so $\Bbb Q(\sqrt{3+2\sqrt2})=\Bbb Q(1+\sqrt2)=\Bbb Q(\sqrt2)$.
Jan
19
comment Proof in Propositional Logic of Peirce's Law
Just enclose them between $ signs. Also, use \phi and \psi. Btw, exactly what 'basic axioms' do you refer here?
Jan
19
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