The point is you don’t start with definitions, you start with problems. Nobody ever had an

The point is you don’t start with definitions, you start with problems. Nobody ever had an
idea of a number being “irrational” until Pythagoras attempted to measure the diagonal
of a square and discovered that it could not be represented as a fraction.
Definitions make sense when a point is reached in your argument which makes the
distinction necessary. To make definitions without motivation is more likely to cause confusion.