What is $ \mathfrak{c} $?

\mathfrak{c} is the size of all the numbers between 0 and 1, like the numbers on a ruler that goes from one end to the other.

Imagine you have a bag full of tiny jellybeans, each labeled with a number from 0 to 1. Now picture another bag, but this time it's full of all the numbers you can think of, like 1, 2, 3, or even numbers that go on forever like π (pi). Surprisingly, both bags have the same amount of jellybeans!

But \mathfrak{c} is different. It’s like a bag with so many jellybeans that it's harder to count, in fact, there are more jellybeans in this special bag than there are in the whole number bag.

\mathfrak{c} is called the cardinality of the continuum, and it’s equal to 2^{\aleph_0}, which is like saying you take all the numbers from 0 to 1 and multiply them by themselves an infinite number of times.

It's a way to describe how many tiny pieces fit into a line, something really small can have a lot of stuff inside it!\mathfrak{c} is the size of all the numbers between 0 and 1, like the numbers on a ruler that goes from one end to the other.

Imagine you have a bag full of tiny jellybeans, each labeled with a number from 0 to 1. Now picture another bag, but this time it's full of all the numbers you can think of, like 1, 2, 3, or even numbers that go on forever like π (pi). Surprisingly, both bags have the same amount of jellybeans!

But \mathfrak{c} is different. It’s like a bag with so many jellybeans that it's harder to count, in fact, there are more jellybeans in this special bag than there are in the whole number bag.