Prove that the function $f:(Z_{+} \times Z_{+}) \rightarrow Z_{+}^{*}$ and $f(x;y)=2^{y}(2x+1)$ is bijective.
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
81546
Prove that function from $S^n \times S^m \to 2S^{m+n+1}$ is immersion
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
67644
How does one get the formula for this bijection from $\mathbb{N}\times\mathbb{N}$ onto $\mathbb{N}$?
130137
How to define a Bijection between $(A^B)^C$ and $A^{B \times C}$
84301
Showing that some Function on the Unit Disc is injective
22869
Prove $[0, 1]$ and $(0, 1]$ are equinumerous by use of bijection
40868
Composition of two functions - Bijection
121729
Prove without using graphing calculators that $f: \mathbb R\to \mathbb R,\,f(x)=x+\sin x$ is both one-to-one, onto (bijective) function.
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
10307
Show the inverse of a bijective function is bijective
37951
proof detail concerning bijection between a set and its power set
17519
Let $z \in\Bbb{C}^{\times}$ such that $|z^3+\frac{1}{z^3}|\leq 2$. Prove that $|z+\frac{1}{z}|\leq 2$.
145875
Inverse of a bijection f is equal to its derivative
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
21707
Constructing a Bijective function via an injective and surjective one.