TITLE: Countability of a set of partitions
QUESTION [0 upvotes]: I'm trying to figure out if "the set of all possible partitions of the interval [1,0] is countable or uncountable."

REPLY [0 votes]: It is uncountable. For every $x \in [0,1]$, of which there are uncountably many such $x$, $\{ \{x\}, [0,1] \setminus \{x\}\}$ is a partition of $[0,1]$.
{"set_name": "stack_exchange", "score": 0, "question_id": 2508756}