query: Prove that $b\cdot\aleph_0=b$, where b is an infinite set.
positive_passages.docid: 24785
positive_passages.text: How prove this equation $\alpha=\aleph_{0}\alpha$
negative_passages.docid: 48797
negative_passages.text: Proving Two Sets are Equal - Infinite Sets - Example
negative_passages.docid: 144787
negative_passages.text: Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
negative_passages.docid: 145397
negative_passages.text: How to prove that for every $i$, $a_i = i$
negative_passages.docid: 22232
negative_passages.text: Proving that cardinality of the reals = cardinality of $[0,1]$
negative_passages.docid: 98206
negative_passages.text: Let $B\subset\mathbb{R}^d$ be closed and $z\in\mathbb{R}^d$, show that there is $b_0\in B$ such that $\delta(z,B)=\|z-b_0\|$.
negative_passages.docid: 123613
negative_passages.text: Double Complement of a set proof
negative_passages.docid: 64108
negative_passages.text: how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
negative_passages.docid: 151295
negative_passages.text: Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
negative_passages.docid: 92588
negative_passages.text: Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
negative_passages.docid: 45218
negative_passages.text: Comparing the two cardinals $\aleph_0^{\aleph_0}$ and $2^{\aleph_0}$
negative_passages.docid: 70940
negative_passages.text: Homework - set theory infinite union
negative_passages.docid: 33233
negative_passages.text: Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 20281
negative_passages.text: Easiest way to prove that $2^{\aleph_0} = c$
negative_passages.docid: 144372
negative_passages.text: How to Prove that if $A$ is bounded, then $A \cdot A$ is bounded?
negative_passages.docid: 109070
negative_passages.text: Question about the proof of the distributive property for sets