Bijective proof

Okay kiddo, so let me explain what bijective proof means in a way that's easy to understand.

A bijective proof is like playing with two sets of toys where all the toys have a pair. Let's say you have a set of five toys and your friend has another set of five toys. If you can match each one of your toys with one and only one of your friend's toys, and your friend can do the same, that's called a bijective relationship.

Now, think of numbers instead of toys. If you have a set of numbers and your friend has another set of numbers, and you can match each of your numbers with a number from your friend's set and vice versa (meaning every number has a match and no number is left out), that's also a bijective relationship.

But what does bijective proof mean? It means you can use this matching relationship between sets to prove something is true with math. For instance, let's say you want to show that there are the same number of even numbers as there are whole numbers. You can use the bijective relationship between the two sets and match each even number to a whole number and vice versa. Since every even number corresponds to one and only one whole number, and every whole number corresponds to one and only one even number, you can prove that the two sets have the same number of elements.

So that's what a bijective proof is, matching pairs of things and proving things true using this relationship.