It's not an infinite loop. Consider this is a standing offer.

$1 for every useless fact you can present.

Well, as soon as you learned a fact you could consider useless, it would get you $1, which meant it was no longer useless. So, at that point, you no longer know any useless facts.

End of loop.

So, while this offer would prevent you from making money off of any useless facts, you can't possibly know an infinite amount of facts, making the number of loops you would pass through finite.

This is, of course, only considering if newly learned facts could be considered for the offer. At the time the offer is made, it immediately nullifies all useless facts into useless facts in one pass. There is no looping. It's just a thing that happens as soon as the offer is made.