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

It is true, take for example a function $f:\mathbb{Z} \to [0,1]$ $$f(n)=\cases{{1\over 2|n|+1};\;\;\; n\leq0\\{1\over 2n};\;\;\; n>0}$$
