Detemine cardinality of $ \{ f: \mathbb{N} \rightarrow [0,1] \}$

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Detemine cardinality of $ \{f \mid f: \mathbb{N} \rightarrow [0,1] \}$.

We can show ran$(f) \neq [0,1] $ by a diagonal argument. But I am not sure how to use this to determine the cardinality.