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one does not get an infinite number of combinations from a finite set of elements, unless we allow for no restriction in word size. it's unclear to me whether this was originally meant poetically. but, it's just simply and quite literally wrong, and well within the limit of pascal's math to figure out.

if you have an alphabet of n letters and a maximum word length of m then you have n^m word combinations. you need to set these restrictions abstractly, but they rather obviously exist. we could reasonably set m by calculating how large it would need to be to generate a new word every second of a one hundred year life span, or simply by doubling the longest known word.

or, consider a language composed of words that take five minutes to pronounce and have dramatically different meanings brought on by minor syllabic changes - an s at two minutes means you're hungry, and it's absence means you're angry. i doubt humans would have the capacity to understand this. rather, we'd be preparing food for angry people, and consoling hungry people. we can't even figure out sarcasm over the internet.

to be serious in this, bounds need to be constructed. they could be arbitrarily large, even. consider a word that has x letters, where x is the number of seconds since the big bang. and consider a language with x sounds. now, consider a sentence with x words - and a book with x sentences. then even consider x books. you're still bounded by x raised to itself numerous times. and that remains finite.

so, those that argue that you can't jump from the finite to the infinite are conceptually correct, but they're drawing the wrong conclusion. what that means is that this idea of digital infinity is incoherent, not that it appeared without precedent. — Preceding unsigned comment added by 198.48.181.80 (talk) 00:39, 10 July 2015 (UTC)Reply

^ Thank you for posting this, how can you get infinity from a finite set of inputs, the burden is on the them to clarify this anomaly mathematically. This really sounds anti-intellectual, or at the very least anti-mathematical. Is anyone able to add clarification on how this is logically consistent? Or is it indeed just a turn of phrase? 114.30.102.74 (talk) 07:24, 20 June 2018 (UTC)Reply

No, there is no *principled* limit to the length of words, or more relevant to this article (which is not about morphology), to the length of sentences. Of course there's a *practical* limit imposed by lifetimes or the age of the universe, but that does not imply that the theory of language needs to impose a limit of sentences that can be uttered in X seconds. God can certainly utter longer sentences (and your belief or not in Him does not alter the argument). Mcswell (talk) 17:38, 8 November 2017 (UTC)Reply