= Cardinality of total orders on a countably infinite set
{title2=$2^{\aleph_0}$}
There are at most continuum many <binary relations> on a <countable set>. For the matching lower bound, order the blocks $\{2n,2n+1\}$ by their index and independently choose the internal comparison in each block. A <binary sequence> determines those choices and distinct <sequences> give distinct labelled <total orders>. The resulting <order types> can all coincide; the count concerns relations, not <isomorphism> classes.
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