Bachmann–Howard ordinal
Alright kiddo, picture a big line with a lot of numbers on it. This line goes on forever and never ends, like counting 1, 2, 3, 4, and so on. This line is called the ordinal numbers, and they tell you the position or order of things, kind of like a scoreboard.
Now, there are some special ordinal numbers that are really big and hard to understand. One of these special numbers is called the Bachmann-Howard ordinal. It's like a superstar in the world of math because it's so big and important.
To understand how big the Bachmann-Howard ordinal is, we need to do something called "recursive definition." This means we use a formula to define the ordinal number, which is kind of like following a recipe. So, hang in there with me, little buddy.
To define the Bachmann-Howard ordinal, we start with a simple number called "omega," which is basically the first infinite number. Then we play a game. We take omega and add one to it, then raise it to the power of itself. Then we do it again, take the answer we just got, add one to it, and raise it to the power of itself. We keep doing this game over and over, adding one each time and raising it to the power of itself.
Now, let's say we keep playing the game forever. We never stop. The result we get after playing this game infinite times is called the Bachmann-Howard ordinal. And it's REALLY big. Like, so big we can't even begin to count how many digits it has. It's like trying to count every single grain of sand on a beach. It's just too big for us to comprehend.
So there you have it, kiddo. The Bachmann-Howard ordinal is a super-big number that's made by playing a game with infinite recursion. It's like a superstar in the world of math, and it helps us understand really big things. Now, go play and have fun!
Now, there are some special ordinal numbers that are really big and hard to understand. One of these special numbers is called the Bachmann-Howard ordinal. It's like a superstar in the world of math because it's so big and important.
To understand how big the Bachmann-Howard ordinal is, we need to do something called "recursive definition." This means we use a formula to define the ordinal number, which is kind of like following a recipe. So, hang in there with me, little buddy.
To define the Bachmann-Howard ordinal, we start with a simple number called "omega," which is basically the first infinite number. Then we play a game. We take omega and add one to it, then raise it to the power of itself. Then we do it again, take the answer we just got, add one to it, and raise it to the power of itself. We keep doing this game over and over, adding one each time and raising it to the power of itself.
Now, let's say we keep playing the game forever. We never stop. The result we get after playing this game infinite times is called the Bachmann-Howard ordinal. And it's REALLY big. Like, so big we can't even begin to count how many digits it has. It's like trying to count every single grain of sand on a beach. It's just too big for us to comprehend.
So there you have it, kiddo. The Bachmann-Howard ordinal is a super-big number that's made by playing a game with infinite recursion. It's like a superstar in the world of math, and it helps us understand really big things. Now, go play and have fun!