Does 0.999... Equal 1?

[steven787]

Rath said:
I don't see what you're basing your argument on Steven.

0.(3) is a single number in the set of real numbers and 0.(3)=0.(3) always, there are no exceptions.

The idea that 0.(3) is only close to 1/3 is because of a lack of understanding of the concept of infinity - the idea that if you multiply 0.(3) by 10 that at the end of all the threes there is now a zero. This ignores the fact that there is no end of all those threes, the number of threes was infinite and is still infinite.

Here is a source with some fairly well qualified people reinforcing this - http://www.newton.dep.anl.gov/askasci/math99/math99167.htm

Couldn't find a better source in the time I could be bothered looking it up.

The idea that .(3) is only close to 1/3 is because of an understanding in the usefulness of computational viability.

The reason why .(3) ≠ 1/3 is because that  1/3*1/10^∞ that is missing.   1/3 IS NOT .(3), it's approximately .(3).  Because of infinity.  Infinite repetition defines the decimal representation as inaccurate.

.(3) is not always .(3), why? Because .(3) is ambiguous.  Some times it is used as an exact representation of .(3), othertimes it is an approximation of the decimal value of 1/3.

Theoretical Mathematicians tend to support the idea that .(3) is close enough.  Applied Mathematicians (the ones who count - get it. Ha!) actually use numbers to do things in the real world do not accept .(3) as an accurate measure of 1/3.

The idea that .(3) + .(3) + .(3) = .(9) AND 1 is ridiculous.  It's basically saying, "Oh well, we can't figure out a better way to express it, so it must be right."  It's not.

Proofing it does not prove the real world values .(9) and 1 are the same.  It just proves that the methods are flawed.

But it's the best system we have, so we don't throw it out.  Pretending it does not have problems is counter productive.  This is an attempt to give quantitative identity to the universe, not a religion taken on faith.

My background is in economics (my Minor), so I am biased.  My position is that all things can be represented numerically, just because we haven't figured out how does not mean we should quit or make shit up.

Edit: I forgot to mention that the concept of infinity isn't proven to exist.  The universe is not infinite, and once we leave our universe there's either a totally different set of values or a different set of rules.  Likewise, when decending in scale, infinity isn't proven either; I do not buy infinitely divisible particle theories.  So sooner or later those 1/3's are going to end in something other than 3.