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A little more on 0.999....
Posted:
May 17, 2006 3:08 PM



One of the things I use in my classes to try to convince my students that 0.999... really does equal one and not just approach it is this:
1. Between any two numbers there is another number, would you agree? (The real numbers are dense.) You can easily find one such number by just adding them up and dividing by 2.
2. If 0.999... is less than 1, then it would be to the left of 1 on the number line, right? (Draw a picture.)
3. OK. How would you write the number between 0.9999... and 1?
It is amazing how this convinces students that the numbers must really be equal, while the proof using the sum of the geometric series doesn't convince them.
Bret Taylor Math Faculty LakeSumter Community College
John 3:30



