query: Prove $n^{\aleph_0} =c= \aleph_0^{\aleph_0}$
positive_passages.docid: 18802
positive_passages.text: Cardinal Arithmetic Example Wikipedia
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$
negative_passages.docid: 20964
negative_passages.text: Proof that $n^2 < 2^n$
negative_passages.docid: 110103
negative_passages.text: Prove that there are $0<c_1 < c_2<1$ s.t. $\frac{1}{g'(c_1)}+\frac{1}{g'(c_2)}=2$ . The same for $g'(c_1)g'(c_2)=1$.
negative_passages.docid: 80876
negative_passages.text: Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
negative_passages.docid: 45218
negative_passages.text: Comparing the two cardinals $\aleph_0^{\aleph_0}$ and $2^{\aleph_0}$
negative_passages.docid: 89175
negative_passages.text: Proof of $(a+b)^{n+1}$
negative_passages.docid: 104124
negative_passages.text: Prove or disprove: $A-(B-C) = (A-B)-C$
negative_passages.docid: 95852
negative_passages.text: Prove that $(a+b)(b+c)(c+a) \ge8$
negative_passages.docid: 52135
negative_passages.text: Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
negative_passages.docid: 55210
negative_passages.text: Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
negative_passages.docid: 110310
negative_passages.text: $|x_{n+1} - x_n| \le C |x_n - x_{n-1}|.$ Prove $(x_n)$ is cauchy
negative_passages.docid: 90438
negative_passages.text: To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
negative_passages.docid: 12954
negative_passages.text: Prove if $ac>bc$ and $c>0$, then $a>b$
negative_passages.docid: 30835
negative_passages.text: Logarithm proof problem: $a^{\log_b c} = c^{\log_b a}$