Ordered Triples and Set Theory

elementary-set-theory

If you try to write $(a,a,b)$ as $\{\{a\},\{a,a\},\{a,a,b\}\}$, removing duplicate set elements simplifies it to $\{\{a\},\{a\},\{a,b\}\}$ and then to $\{\{a\},\{a,b\}\}$.

Similarly if you try to write $(a,b,b)$ as $\{\{a\},\{a,b\},\{a,b,b\}\}$, removing duplicate set elements simplifies it to $\{\{a\},\{a,b\},\{a,b\}\}$ and then to $\{\{a\},\{a,b\}\}$.

So this method risks different ordered triples appearing to be the same

Limit involving floor function: $\lim\limits_{x\to 0} x \left\lfloor\frac1x \right\rfloor$ [duplicate]

Ring with finitely many zerodivisors

Simple solving Skanavi book exercise: $\sqrt[3]{9+\sqrt{80}}+\sqrt[3]{9-\sqrt{80}}$ [closed]

Integral of Bessel function multiplied with sine $\int_0^\infty J_0(bx) \sin(ax) dx$.

square root of a real matrix

Two matrices that are not similar have (almost) same eigenvalues

Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?

Countable Product of Sequentially Compact spaces is Sequentially Compact

A Stirling number identity representing the second-order Eulerian numbers.

Proving that the following series is convergent: $\sum\limits_{i=1}^\infty \left({n^2+1\over n^2+n+1}\right)^{n^2}$

Where would the four normals be?