On: Inventing an Operation to Solve x^x = y (2000)

[a1369209993]

What is ε? The original problem is about natural numbers (ie nonnegative/unsigned integers).

[AnimalMuppet → a1369209993]

Well then, f(x + 1) > f(x). I don't know where you're getting this x < f(x) as "increasing".

The point about sqrt(3) not working for the naturals is a valid point, however.

[a1369209993 → AnimalMuppet]

> Well then, f(x + 1) > f(x). I don't know where you're getting this x < f(x) as "increasing".

Headdesk Yes, that's correct; I misparsed "increasing functions f" as "functions f that increase [the value passed through them]" and then got distracted by the discrete vs continuous confusion.

[AnimalMuppet → a1369209993]

Well, I missed that the domain was N, so... let's both just blame the tryptophan and call it good.

[JoshuaDavid → a1369209993]

ε is epsilon, conventionally "an arbitrarily small positive number".