Metric

Distance defines position

Distance imposes separation.

Separation fixes position.

Position exists through interval.

No location exists without distance.

Nothing occupies space without constraint.

Positions exist only among separated locations.

Distance separates every position.

If separation fails, no position remains.

Intervals exist between positions.

Intervals maintain separation across space.

If intervals collapse, no position is defined.

Distance remains stable across positions.

Stable distance fixes separation.

If distance varies without constraint, separation does not persist.

Objects occupy positions through distance.

Position depends on fixed interval.

If interval fails, no object remains located.

Motion occurs through distance.

Displacement requires separation between positions.

If separation does not persist, displacement does not occur.

Trajectories extend across distance.

Paths require continuous separation.

If continuity fails, no trajectory exists.

Distance restricts relative position.

Positions remain fixed by separation.

If separation fails, positions do not remain ordered.

Intervals remain consistent across positions.

Consistency maintains separation across intervals.

If consistency fails, no interval persists.

Distance sustains all separation across positions.

Separation sustains every possible position.

If distance fails, no position remains.

If distance fails, separation fails.

If separation fails, position does not exist.

If position does not exist, no relation exists.

Without relation, no structure remains.

Distance remains.

Without distance, nothing occupies position.