## Capturing Infinity

Does 0.999 recurring into infinity equal 1 or does it never quite reach 1?

Drag and highlight below for the answer and a proof.

> Yes, it equals 1 due to the nature of infinity.

Here is a proof. Take it so far to a level of recurring.

n = 0.999 and multiply by 10 = 9.999

[Notice the fourth nine added! That's the clever recurring bit towards infinity along the next tenth]

10n minus 1n is 9n.

So 9.999 - 0.999 = 9

Therefore n = 1 and thus, for infinity, 0.999 recurring does equal 1.

Here is a thought. One infinitely living monkey (random agent) sets out on a typewriter to produce a spotless Hamlet. When he gets it wrong, he starts again. The chance it will produce Hamlet is both about as zero and yet completely likely or 1. How come?

> The further a monkey is expected to write without error, the less likely will it produce the spotless full text from the keyboard - so very near to zero for the length of Hamlet in practice - but in infinity the monkey will do it, that is completely likely in theory. The probability of the next keypress being correct is the same as the last keypress being correct, however, or indeed pressing any predicted key.

Adrian Worsfold

Pluralist - Liberal and Thoughtful