query: Show that $F(B)=B$and $F(C)=C$ if $F: \mathcal{P}A \to \mathcal{P}A$ and that $F$ has the monotonicity property
positive_passages.docid: 147934
positive_passages.text: On Tarski-Knaster theorem
negative_passages.docid: 80421
negative_passages.text: Show that $a - b \mid f(a) - f(b)$
negative_passages.docid: 151038
negative_passages.text: How to prove (A v B), (A → C), (B → D) therefore (C v D)
negative_passages.docid: 104044
negative_passages.text: Prove continuous functions $f$ and $g$ are equal
negative_passages.docid: 18905
negative_passages.text: $f(a)=f(b)=f_{+}'(a)=f_{-}'(b)=0$ and $|f''(x)|\le M$. Show that $|f(x)|\le \frac{M(b-a)^2}{16}$.
negative_passages.docid: 65534
negative_passages.text: Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
negative_passages.docid: 102553
negative_passages.text: How to show that $f(z) = f(i)$
negative_passages.docid: 26207
negative_passages.text: If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 16092
negative_passages.text: How to prove that the composition of two surjective functions is surjective
negative_passages.docid: 97184
negative_passages.text: Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
negative_passages.docid: 23125
negative_passages.text: Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
negative_passages.docid: 117418
negative_passages.text: Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
negative_passages.docid: 56413
negative_passages.text: $f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
negative_passages.docid: 60348
negative_passages.text: How do I prove $F(a)=F(a^2)?$
negative_passages.docid: 137626
negative_passages.text: If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
negative_passages.docid: 124868
negative_passages.text: Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$