Transfinite induction
Transfinite induction is a way of talking about things that go on forever, like counting numbers up to infinity. It's like counting to 100 but with bigger numbers and never stopping.
Imagine you have a bunch of toy blocks, and you want to know how many there are. If you just count them one-by-one, you might never finish. But with transfinite induction, you can count them in a really clever way.
You start by picking a really big number—let's say it's 1000. Then you count the number of blocks one-by-one until you get to 1000. When you reach 1000, you know that all the blocks up to 1000 have been counted.
Now we can use that information to do something different. We can say, "I know there are at least 1000 blocks, or something bigger than 1000. If I add one more block to the pile, there will be at least one more than 1000."
That's how transfinite induction works. We take information that we have and use it to figure out something new. This way, we can keep counting larger and larger numbers, forever.
Imagine you have a bunch of toy blocks, and you want to know how many there are. If you just count them one-by-one, you might never finish. But with transfinite induction, you can count them in a really clever way.
You start by picking a really big number—let's say it's 1000. Then you count the number of blocks one-by-one until you get to 1000. When you reach 1000, you know that all the blocks up to 1000 have been counted.
Now we can use that information to do something different. We can say, "I know there are at least 1000 blocks, or something bigger than 1000. If I add one more block to the pile, there will be at least one more than 1000."
That's how transfinite induction works. We take information that we have and use it to figure out something new. This way, we can keep counting larger and larger numbers, forever.
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