Teeqoz said:
It's not just a flaw with base 10 though. Base 3 also has fractions that can only be represented by infinitely recurring decimals. The only thing that changes when you change the base is what fractions. If there is a system that has a flaw, then it's the decimal system itself. However I like to think of it as just another way of writing the same thing. 2/2 (As a fraction), 10^0, 1, 0.999.... All just different ways to write the value (not the number) 1. The recurring 9 notation works for all finite sequences of numbers as well (ie 0.25=0.24999....) It's like a synonym in language. It's just that people are a bit more stuck up when it comes to math. It may be a flaw in the system, but the flaw isn't that this should be incorrect, because it is correct. The flaw is that notation like this is ever used/ever has to be used. However when you denounce something as "simply the result of a flaw in the system", people are often quick to think "aha, so it's not actually correct", so you have to be careful when proclaiming things as the result of a flaw in the system. |
I don't believe I said that the system is flawed. I said it is limited which I'll stand by. That's not to say other systems are not limited (I chose to use base 3 instead of base 2 because 1/3 and 2/3 still repeat there), but this particular example is one that exists in base 10 and not in other systems.