0.99999~ = 1 ?

Yeah, but finitism is silly.

I'll not disagree Edited by cavediver, : No reason given.

It's far worse than that! Let's say that for each Planck volume, you are given another entire universe!! And for each Planck volume in that universe, you are given *another* universe!! You would still not have enough Planck volumes to even begin to write out Graham's number

Read through that again.You meant to say "if for every (positive) number e, |a - b| < e".Or possibly you meant to say "if there is no (positive) number e such that |a - b| > e".Edited by Dr Adequate, : No reason given.

It's funny, no-one has any difficulty with grasping that 1/2 and 2/4 are the same thing.Well, here we have a similar situation. We happen to use a system of notation in which sometimes there is more than one way to write exactly the same number.Edited by Dr Adequate, : No reason given.

Ah, Graham's number isn't that big, it's less than Graham's number + 1. In fact most numbers are probably bigger than it.

This whole Constructivist thing confuses me, I hope you can help.Surely constructivism assumes a somewhat Platonist view. If you are being a total formalist then the rules/axioms of infinite series are consistent and that's all it means for 0.999.... to exist. That is, it is a game of symbols and rules which doesn't contradict itself. In order to say 0.9999.... doesn't exist, you need to think there was an objective mathematical reality and only constructive methods get you there.If you know, what do constructivists think of standard math? Do they believe what is constructive is Platonically true and anything else is just formalist games with pen and paper?Usually I would be skeptical about such a philosophy, however Edward Nelson is a constructivist and he's no fool. (He took the first real hard steps toward showing Quantum Field Theory makes sense mathematically.)

Well It appears that the genaral consensus amongst those who are more mathematically literate than myself is that I am wrong.In which case I stand corrected. And in which case I will need to find a new nomenclature for expressing all but certain without the philosophical possibility of complete and absolute certainty.But just to be clear is it false to say that 0.999R < 1?

This is a genuine question. As it appears that my understanding up until now has been incomplete (to put it politely - or just wrong if we are to be more blunt.But is it wrong to say that 0.999R <1?

Well up until now I have (rightly or wrongly) been expressing the difference between probablistic certainty or otherwise as the differnce between 1 and NOT 1. Where (in my mind at least) 0.999R is not equal to 1.It appears I am need to change my nomenclature. But I am not sure what I should use instead? Well I get what you are saying. I think. But it still seems counter-intuitive that 1/0.999R is entirely equal to 1/1. For example.

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But is it wrong to say that 0.999R <1?

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I'm afraid that it is. Unless you can show that 1 - 0.999R is greater than zero.(Hint: What is the decimal expansion of 1 - 0.999R. How far do you have to go to find a non-zero digit ?)

Double post. See below.Edited by Straggler, : No reason given.

Yeah I am starting to get that despite inbuilt resistance. Can it be shown mathematically that 1 - 0.999R is equal to zero? One step further down the infinite chain than you need to go to make 0.999R the same as 1?

Yes, since they are the same. How many steps does an infinte chain contain then? And what is infinity + 1?

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I hunt for the truthI am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

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Can it be shown mathematically that 1 - 0.999R is equal to zero?

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Yes we can show that there is no number between it and zero, for instance (you can get that from the fact that there is no number between 1 and 0.999R)

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One step further down the infinite chain than you need to go to make 0.999R the same as 1?

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Nice attempt to turn it around. However, would you agree that 1 - 0.999R is zero to an infinite precision ?