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Yes, it is. All you need to do is to ensure that there is no repeating pattern in the digits. You could use random numbers to generate a sequence of 1s and 2s but unfortunately, most of these are actually pseudo-random number generators: they generate sequences which pass the tests for randomness up to a point but eventually fail. You could try linking the decision the hoice of 1s and 2s to tosses of a coin or to radioactive decay which are random.

Alternatively, you could try

1.21121112111121111121111112... where the length of the string of 1s increases by 1 between the 2s.

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Q: Is it possible to build an irrational number whose decimal digits are just 1's and 2's?
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