Prove that 3.999... = 4

(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...