query: Suppose that f is a function from A to B, where A and B are finite sets |A| = |B|. Show that f is one-to-one if and only if it is onto.
positive_passages.docid: 45792
positive_passages.text: Rigorous proof that surjectivity implies injectivity for finite sets
negative_passages.docid: 152057
negative_passages.text: Let $(X,d)$ be a compact metric space. Let $f: X \to X$ be such that $d(f(x),f(y)) = d(x,y)$ for all $x,y \in X$. Show that $f $ is onto (surjective).
negative_passages.docid: 2072
negative_passages.text: Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
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: 88201
negative_passages.text: Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.
negative_passages.docid: 61782
negative_passages.text: How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
negative_passages.docid: 145873
negative_passages.text: Let $X$ and $Y$ be finite sets. Then the set $Y^X$ is finite and $\#(Y^X) = (\#Y)^{\#X}$.
negative_passages.docid: 32525
negative_passages.text: If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
negative_passages.docid: 50012
negative_passages.text: $f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
negative_passages.docid: 99827
negative_passages.text: For what values will f(x) be necessarily one-one?
negative_passages.docid: 152841
negative_passages.text: I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
negative_passages.docid: 7858
negative_passages.text: Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
negative_passages.docid: 19355
negative_passages.text: prove $f(x)=x^3+x$ is one to one and onto
negative_passages.docid: 98271
negative_passages.text: Why does $(x \to a) ≠ (x = a)$ , But $f(x \to a) = f(x = a)$
negative_passages.docid: 101042
negative_passages.text: Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
negative_passages.docid: 134914
negative_passages.text: Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
negative_passages.docid: 111129
negative_passages.text: Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.