Law of trichotomy is that for any two cardinals $a$ and $b$, exactly one of the conditions $a<b$, $a=b$, or $a>b$ holds.

I have the problem $$\arccos\left(\cos \left(-\frac{7\pi}{10}\right)\right)$$ But I am confused on it. What I did: find reference angle, which is $\frac{3...

Gödel's second incompleteness applies, for instance, to r.e. extensions of PA. I am wondering if it applies more generally to arithmetically definabl...

$\forall$ real $r \gt 0$, $\exists$ and natural number $M$ such that $\forall$ natural numbers $n>M$, $0 \lt \frac{1}{n} \lt r$ I think I understand th...

let $T_A:\mathbb R^n\to \mathbb R^n$, and $A$ is vector in $\mathbb R^n$ such that $$T_A(X)=X+A$$ $T_A$ is called the translation by $A$, but I don't...

I've seen the following (e.g. here): I've learned a bit about groups and I could give examples of groups, but when reading the given table, I co...

eStoY confUSo Why didn't he use the dot product? I'm hoping that $\mathbb P_2$ is a polynomial space (I don't even know what that means), p...

Find all eigenvalues and corresponding eigenvectors for the matrix: $$ \left(\begin{array}{cr} 0&-1 \\ 2&3 \end{array}\right) $$ Not looking for a...

I just started studying logic (high school) anyway...for the truth table of logical implication If sentence $A$ is true and $B$ is true then $A\implies B$...

In a recent post I asked what are the ways a continuous function cannot be smooth. Apparently my question was not well posed, but since I am still thinkin...