What are metric spaces?

A metric space is a place where we can measure how far apart things are from each other, like in a playground.

Imagine you and your friend are playing on a big map of the playground, and you want to know how far it is from one swing to another. In a metric space, every pair of things (like swings, slides, or even people) has a number that tells you exactly how far apart they are, this number is called the distance.

In a normal playground, you might just guess how far something is. But in a metric space, there are rules:

• The distance from one swing to another is always the same as the distance from that other swing back to the first one.
• If you go from one swing to another and then to a third, it can't be shorter than going straight from the first to the third.

Think of your backpack. Every time you put something in it, you can measure how heavy it is, that’s like measuring distance in a metric space! The heavier your backpack gets, the farther it feels to carry it. So your backpack is like a metric space where weight is the distance.