User blog comment:Wythagoras/All my stuff/@comment-10429372-20130718073726/@comment-1605058-20130718195432

Are you able to describe a construction of infinitely many sentences of 1000-character strings, each describing different integer? For me, it is impossible, from finiteness of number of such strings. If your construction would rely on a string which, depending on some other things, has multiple possible outcomes, this string sounds for me to not qualify as definition, so is ignored.