Tag Archives: infinity

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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On Infinite Monkeys and Shakespeare

The infinite monkey theorem is the idea that, given an infinite amount of monkeys, typewriters, paper and time, those monkeys will eventually the entire works of Shakespeare or any given text. The infinite monkey theorem stems from the ideas that given infinite time even nearly impossible events become almost certain and that an infinite string of information will contain an extremely improbable sub-string such as Hamlet, the King James Bible or a portion of pi. Finally, in 2003 University of Plymouth researchers used a £2,000 grant to put the infinite monkey theorem to the test. Using six macaques, a computer keyboard and a radio transmitter to obtain the results. The results after the one month test? No Shakespeare. The monkeys produces five pages containing little more than the letter ‘S’ and the keyboard was made filthy from being used as a receptacle for biological waste by said monkeys, but they taught the researchers that monkeys are not random string generators. Actually, macaques rather like the letter ‘S’.

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