Sorry, just got to bite on this -- but I just looked at the "struggles" blog, and saw it is currently active -- and a highlighted quote is this:

**"Not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts"**

https://www.physicsforums.com/insights/struggles-continuum-part-4/

This seems to go to exactly the point of my "cut on a cut" exploration -- in that this approach opens up a recursive cascade of decimal places, where each level of decimal place functions as a bounded interval with a lowest and highest value -- with a range of uncertainty extending between them -- and of course, all these decimal place intervals are all "finitely equal" -- and can all be understood as recursively nested stand-alone unit intervals defined as a boundary-value range -- with "the continuum" defined as that unknowable uncertainty "one level below" our capacity to finitely measure...

https://www.physicsforums.com/insights/struggles-continuum-part-4/

This seems to go to exactly the point of my "cut on a cut" exploration -- in that this approach opens up a recursive cascade of decimal places, where each level of decimal place functions as a bounded interval with a lowest and highest value -- with a range of uncertainty extending between them -- and of course, all these decimal place intervals are all "finitely equal" -- and can all be understood as recursively nested stand-alone unit intervals defined as a boundary-value range -- with "the continuum" defined as that unknowable uncertainty "one level below" our capacity to finitely measure...