Fast-growing hierarchy
Okay, let's imagine that there's a ladder, and you start at the bottom of the ladder. Each rung of the ladder represents a number, but the numbers start at 0 for the bottom rung, 1 for the rung above that, 2 for the rung above that, and so on. The first rung is number 0, the second rung is number 1, the third rung is number 2, and so on.
Now, a fast-growing hierarchy is like a list of ladders, one for each number. So there's a ladder for the number 0, a ladder for the number 1, a ladder for the number 2, and so on. Each of these ladders is like the first ladder we talked about, with 0 at the bottom rung, 1 for the next rung, 2 for the next rung, and so on.
But here's the interesting part: each ladder is much longer than the one before it. In fact, each ladder is so much longer than the one before it that it's hard to really imagine how long they are.
For example, the ladder for the number 0 might only have 10 rungs. The ladder for the number 1 might have 100 rungs. The ladder for the number 2 might have 1,000 rungs. And the ladder for the number 3 might have 1,000,000 rungs!
As you can see, each ladder grows much faster than the one before it. And that's why it's called a fast-growing hierarchy.
This concept actually has a lot of interesting applications in math and computer science, but for now, just know that it's a way of describing numbers that get bigger and bigger very quickly.
Now, a fast-growing hierarchy is like a list of ladders, one for each number. So there's a ladder for the number 0, a ladder for the number 1, a ladder for the number 2, and so on. Each of these ladders is like the first ladder we talked about, with 0 at the bottom rung, 1 for the next rung, 2 for the next rung, and so on.
But here's the interesting part: each ladder is much longer than the one before it. In fact, each ladder is so much longer than the one before it that it's hard to really imagine how long they are.
For example, the ladder for the number 0 might only have 10 rungs. The ladder for the number 1 might have 100 rungs. The ladder for the number 2 might have 1,000 rungs. And the ladder for the number 3 might have 1,000,000 rungs!
As you can see, each ladder grows much faster than the one before it. And that's why it's called a fast-growing hierarchy.
This concept actually has a lot of interesting applications in math and computer science, but for now, just know that it's a way of describing numbers that get bigger and bigger very quickly.