Intereting Posts

Are Euclidean domains exactly the ones which we can define “mod” on?
How can I solve $\sin(x)=\sin(2x)$?
How to calculate the integral in normal distribution?
Measurable Maps and Continuous Functions
Let $G$ be a group of order $36$ and $H$ be a subgroup of $G$ with order 4. Then which is/are true?
Let $f : \to \mathbb{R}$ be a continuous function and $|f(y)| \leq \frac{1}{2}|f(x)|$. Prove that $f(c) = 0$.
What is the expected number of trials until x successes?
Improper Riemann integral of bounded function is proper integral
History of the Coefficients of Elliptic Curves — Why $a_6$?
Contour integration with semicircular arcs.
Non-circular proof of $\lim_{\theta \to 0}\frac{\sin\theta}{\theta} = 1$
The Definition of the Absolute Value
Proving functions are in $L_1(\mu)$.
Let $R=M_n(D)$, $D$ is a division ring. Prove that every $R-$simple module is isomorphic to each other.
Let $f:A \to B$ and $g:B\to A$ be arbitrary functions.

An almost disjoint family is an infinite collection $\mathcal A$ of infinite subsets of $\omega$ such that for all $A, B \in \mathcal A$, the intersection $A \cap B$ is finite. A mad family is a maximal almost disjoint family.

The free ideal generated by $\mathcal A$ is the collection $\mathcal I(\mathcal A)=\{X \subset \omega: \exists B_1,\dots, B_n \in \mathcal A, m \in \omega(X \subset B_1\cup \dots \cup B_n\cup m)\}$. It’s easy to see that $\mathcal I(\mathcal A)$ is a proper ideal on $\omega$, that is: $\emptyset \in \mathcal I(\mathcal A)$, $\omega \notin \mathcal I(\mathcal A)$ and $\mathcal I(\mathcal A)$ is closed under finite uniions and is closed downwards. This ideal is also free, that is, all finite subsets of $\omega$ belongs to it.

- Meaning of the Axiom of regularity (foundation)
- How can there be alternatives for the foundations of mathematics?
- Why hasn't GCH become a standard axiom of ZFC?
- Formally proving the consistency of a formal theory
- Can forcing push the continuum above a weakly inacessible cardinal?
- Is there such a thing as a countable set with an uncountable subset?

The positive subsets of $\mathcal A$ are defined as the elements of $\mathcal I^*(\mathcal A)=P(\omega)\setminus \mathcal I(\mathcal A)$. Question is: Suppose $X \in \mathcal I^*(\mathcal A)$. Is there a mad family $\mathcal M\supset \mathcal A$ such that $X \in \mathcal I^*(\mathcal M)$?

I tried to apply Zorn’s lemma to define such an $\mathcal M$ but I think it didn’t work.

- Using Axiom of Choice To Find Decreasing Sequences in Linear Orders
- Uses of ordinals
- Medial Limit of Mokobodzki (case of Banach Limit)
- For each extensive, monotone function there exists a closure operator that preserves the closed sets
- How many sorts are there in Terry Tao's set theory?
- The non-existence of non-principal ultrafilters in ZF
- Axiom of Regularity
- Comparing countable models of ZFC

- Uniqueness of Fourier transform in $L^1$
- Rigorous proof that $dx dy=r\ dr\ d\theta$
- NBHM QUESTION 2013 Riemann integration related question
- What's the fastest way to take powers of a square matrix?
- Leibniz rule and Derivations
- For two problems A and B, if A is in P, then A is reducible to B?
- How to prove that $3x^5-12x^4+21x^3-9x+2$ is irreducible over the rationals?
- How do I write $\{3,6,11,18,27,38,…\}$ in set-builder notation?
- Quadratic subfield of cyclotomic field
- Strategies to find the set of functions $f:\mathbb{R}\to\mathbb{R}$ which satisfy a given functional equation
- The Ellipse Problem – finding an ellipse inside a triangle
- How does this technique for solving simultaneous congruences work?
- “Closed” form for $\sum \frac{1}{n^n}$
- Proving that if the semigroup (A, *) is a group, then the relation is an equivalence relation.
- Prove that in an ordered field $(1+x)^n \ge 1 + nx + \frac{n(n-1)}{2}x^2$ for $x \ge 0$