I'd like to throw \(\displaystyle \varepsilon\) and \(\displaystyle \hbar\) into the ring.
There is no smallest positive real number. This fact remains true if you extend the reals to the hyperreals of nonstandard analysis. It's not commonly understood that even in the hyperreals, there is no smallest positive real and
no smallest positive infinitesimal. This is easily proven by noting that if you claim $\varepsilon > 0$ and $\forall x \in \mathbb R$, we have $0 < \varepsilon < x$; then $\frac{\varepsilon}{2}$ is also positive and strictly smaller than $\varepsilon$. So $\varepsilon$ wasn't the smallest positive real after all; and since $\varepsilon$ was an arbitrary positive infinitesimal,
there is no smallest positive infinitesimal in the hyperreals. I only mention this because I've seen the contrary asserted on too many message boards.
ps -- How do we know that $\frac{\varepsilon}{2}$ exists and is a positive hyperreal number? Because the reals, and the hyperreals, are a
field. That's a number system in which you can always divide as long as the divisor isn't zero.
So "the smallest positive real" is simply not well defined, and you can't assign it a variable
in a meaningful way. Any such assignment is meaningless since it does not
refer to anything even in the abstract mathematical world. There's no mathematical context where the idea makes sense.
The symbol $\varepsilon$ is universally understood in math to be an
arbitrary small positive real number; and
not a specific one. Your proposed overloading would be incorrect in the context of established math.
As for $\hbar$, that is a
well-known physical constant whose meaning is
universally understood as such by pretty much
everyone, mathematicians and physicists alike.
Moreover it is
strictly larger than zero, and moreover there is
no claim by physicists that it's the smallest unit of measure in the world; only that it's the scale
below which our equations don't work. The Planck scales (time and space) are statements about the limitations of our theories; and
not statements about the world. The Planck limits are epistemological and not ontological.
So it's bad notation to propose overloading a symbol that the physicists own by universal agreement and that doesn't mean what you'd like it to mean. Let alone that it wouldn't refer to anything.
Well I hope you don't mind my opinionated opinion but your post inspired me to let it all hang out. I noted your smiley so this is offered in a similar lighthearted vein.