Poll: Does 0.99 Recurring = 1
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Soldato
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You can define a number using concepts. Infinity is a concept, an integral is a concept. They are "means to an end", and their alteration of other numbers (since you just are adding together 9, 0.9, 0.09 etc, which are all numbers aren't they?) makes new numbers.
Soldato
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You do realise you contridicted yourself with that?
Run that one by me again, it didn't make sense.
No, you can't cope with the concept of infinity and its properties. Its an error in your understanding.
You say "You can't round up an infinitely long number". Take 1/3 = 0.33r etc
I round that up to 1/2.
Whats the problem with that? I rounded up a number that was infinitely long.
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Nothing is difficult about 9.9r - 0.9r = 9, but what relevance does that have to anything?
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It shows your "method" was completely wrong
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Originally posted by AlphaNumeric
It shows your "method" was completely wrong
How?
Sorry I genuinly don't understand what you're trying to say here; perhaps you could re-explain it?
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Its hard to show you your error in the understanding of maths when every proof thrown at you so far you've denied, so why bother? As I said, email Professor Korner in Cambridge (I'll provide his email if you want) and ask him if Maths can deal with infinities, and does it introduce an inconsistency. He'll set you right, and if you don't beleive him, then nothing anyone can ever say to you will change your mind.
You said :Originally posted by piggott
How?
What on earth does the bit in red go on about?
Originally posted by VDO
^That is wrong. 5*.9r!=4.9r5
For a start, 4.9r5 doesn't exist
ok thats a cop out for a start.
you know what i am getting at, any multiplication of 0.999 other than by 10 means that the final number will be different to 9.
in this instance it is 5
and if it is 5 then the equation doesnt work.
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0.9/2 = 0.45?
1/2 = 1?
Im not claiming to be a Maths legend, I dropped Maths at college because I find it boring most the time, and I don't need it. I enjoy a good debate though.
1/2 = 1?
Im not claiming to be a Maths legend, I dropped Maths at college because I find it boring most the time, and I don't need it. I enjoy a good debate though.
i know theres nothing that any1 can say, not even god himself,
cant convince me .9r = 1 cos it doesnt pure and simple.
In are current maths model it might, in logic it doesn't and in this case logic wins. Are maths model needs to be altered. But theres no point cos theres no need for it.
I agree with all of that except, perhaps, the conclusion you reach.
Where we part is that I'm not suggesting, in all I've said about infinity, that it needs replacing. What I'm suggesting is that when using these constructs, you also need to keep one eye on the assumptions they are based on, and on where they would fall down were it not for the assumptions. In other words, eyes wide open - otherwise all you are doing is mechanistically applying the rules.
I've seen many posts here that satirise the philosophy argument, maybe because they have no counter to it. To be honest, that approach strikes me as very weak. To dismiss something with satire is the refuge of the small-minded.
Calculus (for example) is extremely valuable (though few people will use it in their lives), and I'm not suggesting we just ditch anything that relies on the convenience of the abstract. What I'm suggesting is that mathematicians should not be so rigid in their thinking that they ignore the limitations. Use the tools, be it calculus or anything else, but don't trust in them blindly.
That's why I dismiss those that dismiss the "philosophy" approach with cheap shots. Go look at how many mathematical fundamentals have been established by people that were challenging ideas and accepted cant, precisely because they were challenging.
Philosophy isn't, as some seem to think, just some fuzzy, woolly-headed sideline. Philosophy raises some absolutely fundamental questions that ALL mathematicians should keep in mind.
When, for instance, do you accept a proof as proof? Does it require that YOU understand it, or merely that the academic world does? Take Fermat's Last Theorem. As the maths types here will know, Wiles came up with a proof. But, was his proof correct? Do you accept it, and if so, why? Do you understand it yourself? If not, suppose the people that checked it made a mistake. After all, his first proof was, initially, accepted yet under subsequent detailed and rigorous checking proved to be flawed. How many people actually fully understand Wiles' proof? It is, after all, substantial in size and very complex in nature. So, when should it be accepted? Does the fact that nobody has yet found the error mean that there isn't one? Or just that it hasn't yet been found?
Whether you call it philosophy or not, that is the nature of philosophy of mathematics.
To those at Cambridge, I'll make a suggestion similar to Alpha. Go have a chat with Dr Robert Hunt about the philosophy of maths and, perhaps, the nature of mathematical proofs. He is, as I understand it, still a Lecturer in the Department of Applied Maths and Theoretical Physics, and a fellow of Christ's College.
Understand the limits. Use the tools, but be aware of the limits - including that of the nature of the concept of infinity. That doesn't mean that you ignore the proofs of 0.9r=1 as provided by Alpha and others, but that you remain aware of the underlying limitations.
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