# Tag Archives: set theory

## Countable and Uncountable Infinity

Hold on to your pants, this might get interesting here. What if I told you that some types of infinity are bigger than other types of infinity? It’s true. Just think about it for a second. The number of positive whole numbers, or natural numbers, is really big, infinite actually, because for the largest number you can think of I can just add one and there’s a bigger number. The set of natural numbers is what’s called “countably infinite” and any set of numbers that can be paired with the set of natural numbers is also considered “countably infinite”. Theoretically, any countable set can have its entire contents listed if the counter were given enough time. However, the set of all real numbers is not countably infinite because for every two values in the set there are infinitely many values between them. In fact, the set of all numbers between 0 and 1 is greater than the set of all natural numbers, that’s what uncountability does.

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