What are hierarchies of transfinite numbers?

There are infinite numbers, and some infinities are bigger than others, like having an endless amount of candies versus an endless amount of candy bags.

Imagine you have a big jar with an infinite number of marbles. That’s one kind of infinity. Now imagine you have another jar, but this time it has an infinite number of jars, each holding an infinite number of marbles. That's a bigger infinity, like having more levels in your candy stash!

These bigger infinities are called transfinite numbers. They help us count things that go on forever, but some go on more forever than others.

Think of it like stacking blocks:

• A small tower has 10 blocks.
• A tall tower has 100 blocks.
• An endless tower has an infinite number of blocks, that’s one kind of transfinite number.
• Now imagine you have an infinite number of towers, each with an infinite number of blocks. That's a higher level of infinity, like stacking candy bags on top of candy bags forever!

So, just like we can count how many candies or blocks we have, we can also count how big the infinities are, and that’s what hierarchies of transfinite numbers mean! There are infinite numbers, and some infinities are bigger than others, like having an endless amount of candies versus an endless amount of candy bags.

Imagine you have a big jar with an infinite number of marbles. That’s one kind of infinity. Now imagine you have another jar, but this time it has an infinite number of jars, each holding an infinite number of marbles. That's a bigger infinity, like having more levels in your candy stash!

These bigger infinities are called transfinite numbers. They help us count things that go on forever, but some go on more forever than others.