$A=\{f |f:\mathbb{Z}_+ \to \{0,1\}\}$ is uncountable

$A=\{f |f:\mathbb{Z}_+ \to \{0,1\}\}$ is uncountable

Consider the set $A=\{f |f:\mathbb{Z}_+ \to \{0,1\}\}$ I need to show that
it is uncountable.
I was trying to find a bijection between $A$ and $\mathbb{R}$ or if i can
show that there is no injection from $A$ to $\mathbb{Z}_+$ then also it'll
work !