- Phrases like "I'll meet you half-way" would be meaningless. People could only reliably meet at destinations, unless those happened to be halfway to somewhere else.
- When travelling between two places, one might cease to exist at any given point along the route. The transportation industry would suffer.
- Crafty bank managers could claim that your money had disappeared when they tried to apply interest to your balance.
Be happy to have the intermediate value theorem in your life.