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Proof (Posted on 2002-05-29) Difficulty: 3 of 5
Prove that 3.999... = 4

See The Solution Submitted by Half-Mad    
Rating: 3.6667 (9 votes)

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re(3): solution is wrong | Comment 29 of 44 |
(In reply to re(2): solution is wrong by Victor Zapana)

Nope; by the same kind of proof used to show that 3.999...=4, you can show that 0.000...01 is zero, if there are infinite zeroes, but if you don't accept this, there is another way of looking at it.

You usually say that two numbers a and b are different, if there exists a certain d such that b lies outside the interval (a-d,a+d). In this case, if you take a=0 and b=0.00...1, you can never find any such d, which leads to accept that a=b.

(The previous is the same as saying that if a and b are different, there exists a number c between them. In this case, for these a and b, you cannot find such a c.)

The classic explanation is that our every day finite experiences do not allow to predict the result of infinite experiments, but don't worry: the same happened to an old philosopher called Zeno...
  Posted by Federico Kereki on 2003-11-28 23:45:27

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