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From my understanding, a partition $F$ of a set $U$ means that $F$ is pairwise disjoint, and $\bigcup F=U$, and empty set is not in $F$. So if $U=\{1,2,3\}$, would $F =\{\{1,2,3\}\}$ counts as a partition? because it is the only set in the set, I don't have to check for its union or anything.

I do understand that $F=\{\{1\},\{2,3\}\}$ would be a partition.

Anne Bauval
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user22712878
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Nov 26 '23 at 06:46
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    If U is a set, and F is partition of U, would F = {U} count as a partition? Another example, if U ={1,2,3,4,6}, F={{1,2,3,4,6}} would this count as a partition of U? – user22712878 Nov 26 '23 at 06:51
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    Please don't pay attention to that bot. Your question was perfectly clear. And the answer is a loud YES. – Anne Bauval Nov 26 '23 at 07:05

1 Answers1

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Yes, if $U$ is a nonempty set then $F:=\{U\}$ is a partition of it.

"I don't have to check for its union or anything": yes you have to, but the three properties are easy to check:

  • $\bigcup F=U$ $\checkmark$
  • $\forall X\in F,\;X\ne\varnothing$, i.e. $U\ne\varnothing$ $\checkmark$
  • $\forall X,Y\in F,\;(X\ne Y\implies X\cap Y=\varnothing)$ (vacuously true indeed) $\checkmark$.
Anne Bauval
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