[eszed]

Thank you, and everyone else who answered (I hope they see this reply). Your distinction between "sequence" and "number", along with the mathematics of 0.333... = 1/3, convinced me - and my mind is successfully blown.

Follow-up: is it the same for other repeating sequence-looking numbers? As in, would 0.9333... = 0.94?

[eigenket]

Its true of numbers whose with a decimal representation which ends in an infinite string of 9s, so 0.939999... = 0.94. This is because we write numbers in base 10. If you write numbers in base 2 its equal to numbers whose binary representation ends with an infinte number of 1s e.g. 0.11111... (base 2) = 1.

[evanb]

0.9333... is equal to 9/10 + 1/30. To get 9/10 + 4/100 I think what you're aiming at is 0.93999...