Hyperfinite set
Imagine you have a bunch of toys in your toy box. If you count them, you will get a certain number like 10 or 20. This number is how many toys you have in your toy box and is called a finite number.
Now, imagine you have a really big toy box with an infinite number of toys inside. This means you have so many toys that you can't count them all like you did before because there are just too many. This is called an infinite set.
A hyperfinite set is like taking that big toy box with an infinite number of toys and putting them in smaller boxes inside the big box. Each smaller box has a finite number of toys inside, just like when you counted the toys in your toy box before. But since there are an infinite number of these smaller boxes inside the big box, when you add up all the finite numbers from each smaller box, you get an infinite number again.
Think of it like having a whole lot of toy boxes with a whole lot of toys in them, but you can still sort them out into smaller groups that you can count one at a time. Even though there are an infinite number of smaller groups, you can still figure out how many toys are in all of them together. This is what a hyperfinite set is all about - grouping together smaller sets that are each finite in size, but still have an infinite number of elements when you put them all together.
Now, imagine you have a really big toy box with an infinite number of toys inside. This means you have so many toys that you can't count them all like you did before because there are just too many. This is called an infinite set.
A hyperfinite set is like taking that big toy box with an infinite number of toys and putting them in smaller boxes inside the big box. Each smaller box has a finite number of toys inside, just like when you counted the toys in your toy box before. But since there are an infinite number of these smaller boxes inside the big box, when you add up all the finite numbers from each smaller box, you get an infinite number again.
Think of it like having a whole lot of toy boxes with a whole lot of toys in them, but you can still sort them out into smaller groups that you can count one at a time. Even though there are an infinite number of smaller groups, you can still figure out how many toys are in all of them together. This is what a hyperfinite set is all about - grouping together smaller sets that are each finite in size, but still have an infinite number of elements when you put them all together.