Intensive and extensive measures.
Very simply, the notions of continuitiy contiguity map onto intensive and extensive measures. First we mus distinguish a measure. In ancient greek this was called a metron or a monas. Anything can be a metron. If i use that thing to measure then i use it extensively. so a metre stick is metron and the extensive measures are metres, dekametres hectometre , kilometers etc.
Now if i divde a metre fractally into smaller units then i measure intensively and the intensive measures are decimetres , centimetres and millimetres etc.
The unit is usually considered to be continuous, but everything outside of the unit is measured discretely by it.