Existence of an injection between $\mathbb{Z}$ and $[0,1]$ Is the statement that there is an injection between $\mathbb{Z}$ and $[0,1]$ true or false
$\mathbb{Z}\xrightarrow{(1-1)} [0,1]$
i've build it on the definition of cardinality that is if $\lvert A \lvert \leq \lvert B \lvert$
then there exists an injection $f:A\longrightarrow B$ and one knows that
$\lvert \mathbb{Z} \lvert \leq \lvert [0,1]\lvert$
thus there exists an injection

Define $f : \mathbb{Z} \rightarrow [0,1]$ by
$$f(n) = \frac{1}{2(n+1)} \quad \quad \text{if} \quad n \geq 0$$
$$f(n) = \frac{1}{1-2n} \quad \quad \text{if} \quad n < 0$$
