Lebesgue's number lemma
Lebesgue's number lemma is like a special recipe for covering things up.
Imagine you have a piece of paper and some stickers that you want to cover the paper with. But you don't want any part of the paper to be showing, so you need to make sure to use the right size stickers that will cover everything.
Lebesgue's number lemma helps you figure out the right size sticker you need to use to cover everything up.
It works like this: if you have a bunch of little pieces of paper that you want to cover up with stickers, but you don't know what size stickers to use, you can use Lebesgue's number lemma to figure it out.
First, you divide the paper into a bunch of smaller pieces. Then, you pick one of those smaller pieces to be your starting point.
Next, you imagine that you're going to cover up that starting piece with a sticker. But you don't want the sticker to go outside of the starting piece or cover up any other parts of the paper.
So, you use Lebesgue's number lemma to figure out the biggest size sticker you can use that will cover up the starting piece without going outside of it.
Once you've figured that out, you can use that same sticker size to cover up all the other little pieces of paper, and you know that your stickers will cover everything up perfectly.
Basically, Lebesgue's number lemma helps you find the perfect size sticker to use when you want to cover up a bunch of little pieces of paper without leaving any gaps or overlaps.
Imagine you have a piece of paper and some stickers that you want to cover the paper with. But you don't want any part of the paper to be showing, so you need to make sure to use the right size stickers that will cover everything.
Lebesgue's number lemma helps you figure out the right size sticker you need to use to cover everything up.
It works like this: if you have a bunch of little pieces of paper that you want to cover up with stickers, but you don't know what size stickers to use, you can use Lebesgue's number lemma to figure it out.
First, you divide the paper into a bunch of smaller pieces. Then, you pick one of those smaller pieces to be your starting point.
Next, you imagine that you're going to cover up that starting piece with a sticker. But you don't want the sticker to go outside of the starting piece or cover up any other parts of the paper.
So, you use Lebesgue's number lemma to figure out the biggest size sticker you can use that will cover up the starting piece without going outside of it.
Once you've figured that out, you can use that same sticker size to cover up all the other little pieces of paper, and you know that your stickers will cover everything up perfectly.
Basically, Lebesgue's number lemma helps you find the perfect size sticker to use when you want to cover up a bunch of little pieces of paper without leaving any gaps or overlaps.