Imagine you have two big boxes, one with all the numbers, and another with just even numbers. At first, it seems like there are more numbers in the first box than even numbers in the second. But if you pair them up (1 with 2, 2 with 4, 3 with 6), they match perfectly! This means both sets of numbers are infinite, and they're the same size of infinity. But sometimes, when we count things like numbers or points on a line, one kind of infinity is actually bigger than another, that’s where the magic starts!
Examples
- If you count all the numbers, then just even numbers, they still match up perfectly, both are infinite!
- Counting whole numbers (1,2,3...) is one kind of infinity. Counting all decimals between 0 and 1 is a bigger infinity.
- Matching every number to an even number shows that both sets have the same size of infinity.
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See also
- Why Do Infinity and Infinity Not Always Add Up?
- Why Does Infinity Keep Changing Shape?
- What Is Infinity — And Why Does It Come In Different Sizes?
- What is continuum?
- What is infinity?