## 5 thoughts on “Why Every Proof that .999… = 1 is Wrong”

1. tsvaishnav says:

While these proofs are quite convincing there is one observation that has been ignored in the above proofs. If you divide any number by 9 you get the pattern. For example 5/9 = 0.55555555……till infinity. So 9 * 0.55555555….. = 5. In same way if we divide 9/9 we get 1 as quotient. But as per the pattern observed it should be 0.99999999…..till infinity. So we can say that 0.999999999….. = 1.

2. Hello Vi Hart.

x = .222222….
10 x = 2.22222222222.
10 x – x = 2
9x = 2
x = 2/9

I agree that in the context of the super infinity,
that .9999999999999999… is infinitesimally < 1.

The set of real numbers is defined exactly to exclude infinitesimals.

It is only because .0000000000000000….1
is not deemed to be a real number,
that we must identify .999999999999999 with 1.

.0000000000000000….1 can be considered to be a unit infinitesimal in
an enlarged arithmetic beyond the real number system.

Kermit

3. tsvaishnav says: