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$\begingroup$ Small issue regarding the first paragraph - What if a person is neither a leader nor a ruler? $\endgroup$
– DanDan面
Commented Jun 5 at 23:29
$\begingroup$ The rest of the proof is really neat though! However I do not believe it generalizes to the uncountably infinite case $\endgroup$
– DanDan面
Commented Jun 5 at 23:30
$\begingroup$ I don't think that matters? We are using the fact that every group must have someone in charge. $\endgroup$
– azi
Commented Jun 5 at 23:31
$\begingroup$ You are right in that the rest of the proof is sound, there is just a slight imprecision in the statement 'every person in the population has to be either a leader or a ruler" $\endgroup$
– DanDan面
Commented Jun 5 at 23:32
$\begingroup$ ah gotcha, thanks! $\endgroup$
– azi
Commented Jun 5 at 23:32

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