Constructive set theory

Why can't you always find the smallest number in a list?

Imagine you're at a party and everyone hands you a different number of candies. You're curious to know who gave you the least amount of candies.

Think of the candies as a collection of numbers. There's always a person who gave you the smallest amount, no matter how many people there are. This idea is guaranteed by a principle in mathematics.

Example

If one person gave you 3 candies, another 7, and a third 2, you can easily spot that the third person gave you the smallest amount.

Remember this

This principle is known as the Well-Ordering Principle, which states that every non-empty set of positive integers has a smallest element.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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