Math CentralQuandaries & Queries


Question from Tom:

Is it possible to build an irrational number with numbers that are just 1's and 2's where only finitely many 2's appear? If so, how do we build it and how do we know it is irrational?


Build any such number and multiply by the appropriate power of 10 to shift the decimal point over to where all that appears after the decimal place is an infinite number of 1's. Build another number that consist of only infinitely many 1's after the decimal point - that's rational.

What can you say about these two numbers you built?



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