Playing with Infinity – Footnote 1

 

You may recall from school arithmetic that the number 2.000000… can also be written with a recurring decimal 9 so that 1.999999… = 2.000000…  Similarly, 0.750000… can also be written as 0.749999… and so on.  So real numbers that have a terminating decimal followed by infinitely many 0s can always be represented by an equivalent decimal expansion with infinitely many trailing 9s.  That doesn’t matter: the important thing is that all real numbers can be represented, and we can choose to use the recurring zeros instead of the recurring 9s.

 

Back to Playing with Infinity