User blog comment:Wythagoras/Finite Promise Games/@comment-10429372-20140829185955/@comment-1605058-20140829191303

The thing with "suffiscently large" is that if, say, m is suffiscently large for soem purpose, then so is every number greater than m. Same goes for s. So if statement holds for all suffiscently large m and s, then we can find pair of equal numbers for m and s which will satisfy the statement.