User blog comment:Edwin Shade/Enumerating the Countable Ordinals/@comment-30754445-20171206034326/@comment-32876686-20171209005047

Couldn't the lowest non-zero element of $$(0,1)$$ be $$\frac{1}{\mathfrak{c}}$$, where $$\mathfrak{c}$$ is the cardinality of the continuum ?

My reasoning is that if the interval $$(0,1)$$ is composed of a $$\mathfrak{c}$$ number of parts, then the smallest portion you can have of that interval is $$\frac{1}{\mathfrak{c}}$$ and hence the smallest non-zero value in that range would be $$\frac{1}{\mathfrak{c}}$$.