[da_chicken]

Of course it does. It's called the infinitesimal. It's common definition for real number is 1 / infinity: https://en.wikipedia.org/wiki/Infinitesimal

If you've taken Calculus, you've already worked with math that requires the infinitesimal to exist.

It's not a value you can meaningfully write out, but you can't write out pi, e, phi, root 2, 1 / 3 in base 10, root -1, etc. "I can't write it down" isn't a particularly unique property for numbers.

[gspr]

> If you've taken Calculus, you've already worked with math that requires the infinitesimal to exist.

Not at all. Standard calculus uses standard real numbers, for which there is no infinitesimal. One may well speak of infinitesimals as a mental tool when building a mental model for calculus, but those infinitesimals are not actual real numbers (or a well-defined mathematical object at all - in standard calculus).

[brlewis]

Correct. This is covered in the article. https://en.wikipedia.org/wiki/0.999...#Infinitesimals

[pwdisswordfish2]

There is no smallest positive infinitesimal either. At least in theories that manage to define those rigorously. And it’s mostly a formal trick anyway; standard epsilon-delta calculus avoids them entirely.

Had you actually meaningfully studied this subject, or did you just link to a Wikipedia article you half-heartedly skimmed one day?

[da_chicken]

That's a funny way to say, "No, I think you misunderstand. I mean to say no single infinitesimal number exists. Like infinity, the concept exists, but as a literal single number, no."

[camelite]

> There is no smallest positive infinitesimal either.

There is in the surreal and hyperreal number systems. I got that from skimming wikipedia though....

[petters]

At the very least, don't write "Of course it does". It does not in the real number system.