No indeterminates in the reals? 
Of course there are indeterminates in the real numbers - can you provide a complete representation in *any* number system for those numbers we call irrational? The answer is no. Even if it were possible for 0.999... to equal 1, it breaks the decimal system as it was intended since its invention. Do you agree that not all real numbers can be represented in a radix system? If yes, why would you insist on having a cauchy sequence define a number?  Just because you can list the first few terms says nothing about the limit. For example, you can provide a Cauchy sequence that 'represents' pi but you cannot find its limit. There are several contradictions in this branch of 'analysis' - All Cauchy sequences must have limits but you cannot find the actual limit of 'most' Cauchy sequences that represent the majority of real numbers you cannot represent completely. I am not calling you an idiot but I am glad that you think you are an idiot. It's the first step to enlightment. Am I logamath? Nope. Not logamath but I am the so-called 'troll' most of your wiki math gods hate. I have the most extreme disdain for Michael Hardy, Krmsq(close runner up bum), Melchoir and small fry like Meni Rosenfield in this order. The rest of you are all pawns who have to support their 'view' of the math-world. 

In the dark ages, we had the leaders of the church who supported only their conception of the universe until someone smart came along and proved them to be all idiots who were hindering the progress of mankind. Likewise, Wikipedia will 'fail'. Hail Knol!! Knowledgeable individuals will be able to post without fools like you trampling all over their pearls. No one on Wikipedia is qualified to edit my work. You first have to know what I know and then you can speak to me on my level. As arrogant as this sounds, Hardy and company are bishops of the math church whose founders were exceptional fools like Cauchy, Weierstrass and the rest who I don't care to mention. 98.195.24.26