Practice question · Multiple choice
The sequence 0.9, 0.99, 0.999, … has limit 1. Does any term equal 1, and does that matter?
Hints
- Ask what the notation 0.999… actually names: a term of the sequence, or the limit?
- If 0.999… were less than 1, name a number strictly between them.
Show the answer
A. No term equals 1 and it does not matter, since 0.999… is the limit
Why
The notation names the limit, not a term, and no number lies strictly between 0.999… and 1, which settles it. The persistent objection assumes the symbol means 'a very long term', and the whole content of a limit is that it means the value being approached.
Practise Limits
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.