= Threshold language
{title2=$L_a=\{\operatorname{enc}(n):n\geq a\}$}
For a fixed <natural number> $a$ and a standard encoding of <natural numbers>, validate the <input> and compare its encoded value with $a$. This decides $L_a$. A <well-ordering> argument can prove that an upward-closed <set> of <natural numbers> has this form without calculating its least element. A decider may contain that fixed least element in its finite description; its existence does not give a uniform method to discover the least element from another program.
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