query: find an injection $h:\{\mathbb{N}\to\{0, 1\}\} \to A$ while A = {f : N → Z|∀n, m ∈ N.(n > m) → (f(n) < f (m))}
positive_passages.docid: 152613
positive_passages.text: Injection from $\mathbb{N}\to\{0,1\}$ to the set of all monotonic decreasing functions from $\mathbb{N}\to\mathbb{Z}$
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$
negative_passages.docid: 113360
negative_passages.text: How many injective functions $f:[1,...,m]\to{[1,...,n]}$ has no fixed point? $(m\le n)$
negative_passages.docid: 24107
negative_passages.text: Bijection $f:\mathcal{P}(A)\to(A\to \{0,1\})$
negative_passages.docid: 46971
negative_passages.text: Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$
negative_passages.docid: 106698
negative_passages.text: $\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
negative_passages.docid: 20199
negative_passages.text: Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
negative_passages.docid: 85032
negative_passages.text: $Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
negative_passages.docid: 132431
negative_passages.text: Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
negative_passages.docid: 23464
negative_passages.text: How to find a explicit bijection for some $f:A\times B \rightarrow B \times A$
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 144890
negative_passages.text: Recurrence $f_{n+2}=af_{n+1}+bf_n$
negative_passages.docid: 39231
negative_passages.text: Construct a bijection between $\mathbb{Z}^+\times \mathbb{Z}^+$ and $\mathbb{Z}^+$
negative_passages.docid: 108921
negative_passages.text: By substituting $z = h(t)$ show that $\delta(h(t))=\sum\limits_{i}\frac{\delta(t−t_i)}{\mid h^{\prime}(t_i)\mid}$
negative_passages.docid: 75614
negative_passages.text: Proving that $n|m\implies f_n|f_m$
negative_passages.docid: 68818
negative_passages.text: $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$
negative_passages.docid: 126821
negative_passages.text: Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$