## Empty basket is a basket of apples, tennis balls, or stars

At school I first learned about the empty set:

An empty set is a subset of any set.

I still remembered being taught simply taking it for granted, and memorizing it correctly on important occasions (e.g. during an exam). Despite how odd the mathematical statement sounded like, I did what I was taught to do.

This is how I makes sense of it. Given a basket of apples, after all apples were taken by some monkeys, the empty basket would still be called a basket of apples, because it’s literally “a basket of apples that contains none at all”. Moreover, suppose someone comes along and doesn’t see what kind of fruits the basket originally contained, then he or she could claim that the very same empty basket a basket of pears, or a basket of tennis balls, etc. So an empty basket could be an basket of any kind of fruits, or items.

How could one actually be sure that a basket is NOT a basket of apples? Well, if one actually sees that the basket contains anything that’s not an apple, for example a star, then he or she must be able to claim that the basket is not of apples, but of stars.

So can one say a given empty basket is NOT a basket of apples? Not really, because it does NOT contain anything that is NOT an apple. Furthermore, it seems to me that one can not even say an empty basket is NOT a basket of bananas, tennis balls, stars, etc, simply because the empty basket does not contain anything!

Knowing that one can not say a given empty basket is not a basket of apples, can one say the opposite is true, that a given empty basket is a basket of apple?

Here where mathematical logic comes in. There is an interesting law called the Law of Excluded Middle, which means a mathematical statement is either true of false, nothing in the middle. So a basket is either a basket of apples or not.

So applying the Law of Excluded Middle, one can safely draw from the fact that one can not say a given empty basket is not a basket of apples, to the conclusion that a given empty basket is a basket of apples.

Substitute apples with anything you like, bananas, tennis balls, stars, black holes, etc. You end up with the same conclusion that a given empty basket cannot be said to NOT be a basket of some things, so it has to be a basket of those things.

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