\(\displaystyle card \: (\mathbb{R}) > card \: (\mathbb{N}) =\infty \).

also an easy fast method is to consider the set of reals as \(\displaystyle \mathbb{R}:\{-\infty , ...,-3 ,-2 ,-1, 1,...,\infty \}\) and \(\displaystyle \mathbb{N}: \{ 1 , 2 , 3 ,...,\infty \}\). which can be seen that reals have larger cardinality .

or write reals as \(\displaystyle \dfrac{n}{10^m } \) and compare the number of values over \(\displaystyle n\).