Why is a set not a partition of itself?

A partition of a set $A$ is a subset of its power set.

$\{\{1,2,3,4\}\}$ is, but $\{1,2,3,4\}$ is not, a partition of $\{1,2,3,4\}$.

$\{1,2,3,4\}$ is an element, not a subset of the power set of $\{1,2,3,4\}$.


a partition of a finite set $S$ is any set $\{S_1, \dots, S_n\}$ of $n$ subsets of $S$...

You answered your own question. Which element of $\{1,2,3,4\}$ is a subset of $\{1,2,3,4\}$?

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Combinatorics

Elementary Set Theory

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