brennan
Argumentative Brit
Great. So you understand perfectly well that it is common practice to accept exceptions for certain numbers in some cases and you can stop pretending that it is ridiculous for me to suggest do so for zero.
1=.999999...?
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Hygro
soundcloud.com/hygro/
It's really weird reading this argument.
"Decimal notation is inherently flawed because it results in bugs like 0.999.... = 1"
"No that can't be, this flawed decimal notation is not flawed because the flaw that gets 0.999... = 1 proves that 0.999 = 1".
Brennan understands that 0.333... is a real number that is identical to the fraction 1/3. He also understands that 0.333... is written in a notation that equals one third because a written process creates an endless string of 3's. He also recognizes that in the logic of reading decimals, devoid any declarative, new-premise statements that say "0.333... = 1/3" will tell you that a decimal point followed by endless 3's cannot be read as exactly 1/3, as it infinitely narrowly undershoots 1/3. That is inherent in the notation. Brennan's critique is of the notation used to describe the math.
It's clear to anyone how 0.999... can be equated to 1. None of that proves that the system to do so didn't just demonstrate a trivial error.
"Decimal notation is inherently flawed because it results in bugs like 0.999.... = 1"
"No that can't be, this flawed decimal notation is not flawed because the flaw that gets 0.999... = 1 proves that 0.999 = 1".
Brennan understands that 0.333... is a real number that is identical to the fraction 1/3. He also understands that 0.333... is written in a notation that equals one third because a written process creates an endless string of 3's. He also recognizes that in the logic of reading decimals, devoid any declarative, new-premise statements that say "0.333... = 1/3" will tell you that a decimal point followed by endless 3's cannot be read as exactly 1/3, as it infinitely narrowly undershoots 1/3. That is inherent in the notation. Brennan's critique is of the notation used to describe the math.
It's clear to anyone how 0.999... can be equated to 1. None of that proves that the system to do so didn't just demonstrate a trivial error.
Terxpahseyton
Nobody
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This is just as bad as the 0.333... = 1/3 "solution". And likewise, it says essentially: Here is why x is true. It is because x is true. Math wizardry people!
Just more symbols.
If you put it like that it would be a weird objection, in deed.
An objection that makes actually sense:
0.999... does not describe a quantity at all, for one. That is just a fact. Forget mathematical rules. If you have any idea what, in terms of quantities, the number 0.999... actually means, then you should be able to recognize the truth of that statement. I feel really silly if this has to be explained. Common sense, man.
1 does describe an exact quantity.
Now that is a rather akward divergence in traits for numbers which are merely supposed to be different styles of writing.
....
Not sure weather I will respond to the responses of my last post. I'd like to, but it looks like so much tedious work
Maybe 
Can somebody please tell me that this is an organized trolling campaign?
Lohrenswald
世界的 bottom ranked physicist
Has anyone tried to put it from this angle?
that assuming 0,999...<1, there would have to be a number that you could add to 0,999.. to get 1
Now the smallest positive number I can think of (in decimal form as of right now...) would be on the form of 0,000...001. So many many zeros and a one. However, we can obviously not have infinitely many zeros befor the one. But we can put infinitely many zeros after the one: 0,000...01000... (I suspect this isn't entierly water thight, but it's better than the counterpoints I'd dare say)
and so we add (keep in mind there are infinite 9's):
0,999...999...+0,000...00100...=1,000...00999999.....>1
because wathever digit the one falls on, it "makes that a ten" and then you now it's added up, but there are still infinitely many 9's after that spot. Even if it's a really small part, this sum get's larger than 1
and so 0,999...=1
(I hope I'm not talking nonsense)
that assuming 0,999...<1, there would have to be a number that you could add to 0,999.. to get 1
Now the smallest positive number I can think of (in decimal form as of right now...) would be on the form of 0,000...001. So many many zeros and a one. However, we can obviously not have infinitely many zeros befor the one. But we can put infinitely many zeros after the one: 0,000...01000... (I suspect this isn't entierly water thight, but it's better than the counterpoints I'd dare say)
and so we add (keep in mind there are infinite 9's):
0,999...999...+0,000...00100...=1,000...00999999.....>1
because wathever digit the one falls on, it "makes that a ten" and then you now it's added up, but there are still infinitely many 9's after that spot. Even if it's a really small part, this sum get's larger than 1
and so 0,999...=1
(I hope I'm not talking nonsense)
Akka
Moody old mage.
Never attribute to malice that which is adequately explained by stupidity.
brennan
Argumentative Brit
To increment up to 1 from 0.999... surely you add 1-0.999...
Lohrenswald
世界的 bottom ranked physicist
brennan
Argumentative Brit
Who told you about the operation?????
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Mathematical facts are objectively true you can't debate them. Everyone here in this thread who believes that 1 =/= 0.999... is literally objectively wrong.
Lohrenswald
世界的 bottom ranked physicist
On closer thought, why do you dispute that 0,999... is a "straightforward" number, but show no qualms about 1-0,999...?
brennan
Argumentative Brit
Pft. You'll be claiming next that 1+1=2 is always true.
What has this got to do with what I think? If you don't have a problem with 0.999... then you can't take issue with 1-0.999...
Lohrenswald
世界的 bottom ranked physicist
how is it not?
Borachio
Way past lunacy
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Look. Just throw out the nines, OK? (It's a recognized technique, after all.)
Then:
1 = 0.999...
(throw out the nines)
1 = 0.000...
Easy, eh?
Then:
1 = 0.999...
(throw out the nines)
1 = 0.000...
Easy, eh?
onejayhawk
Afflicted with reason
Please read my post above. It answers this.
1) See above. A series is the sum of a sequence.
2) A difference which is not defined. It can be described, but there (currently) is no definition.
3) Less than and not equal.
4) Conceded. What was your point?
5) That is the question you should have asked from the start. The answer is that the 0.9+0.09+0.009+... =/= lim (0.9+0.09+0.009+...)
6) Sure they do. Why would they not? There is even a standard notation for it:
lim Σ f (xn
n=1 to infinite
7) If you are defining 0.999... = 1, just say so and stop bothering with so called proofs. That was not a given, see #5. I decline to accept the definition. A series is the sum of all elements of a sequence, not the limit of the sum. The sum and the limit are typically not equal, e.g. 0.999 =/= 1.
What it means is that there are numbers we can describe, but not define. It is like the largest number less than 1, if such a number was defined. It is like the number touching 1, if such a number were defined. It is like the endpoint of an open segment, if such a thing were defined.
This what you deal with in the non-algebraic numbers, which is an uncountable set. If the real numbers continuously map to a line, then there must be continuous points. However, we have no tools or language to manipulate continuous numbers. Instead we find ways to use algebraic numbers as substitutions. Since one set is dense on the other, this works. However, note that the definition of "dense" involves a limit.
In short, this is an exercise in semantics.
J
brennan
Argumentative Brit
Real world examples include:
Go to the supermarket and get two packs of crisps priced at £1.00 each. Go to checkout and they are on offer! 1+1=1
Mixing aggregates of different sizes, including liquids with different molecular weights such as water and alcohol, results in the same phenomenon.
It's called non-diphantine arithmetic. Go look it up.
Lohrenswald
世界的 bottom ranked physicist
You have continously against evidence and very well reason arguments still upheld that 1=/=0,999...
However, dispite of that this right here is the most stupid thing you have said this entire thread
brennan
Argumentative Brit
Yes. But we're talking about your argument so I applied your own rules. Besides, as has been pointed out the arguments seem to boil down to 'we defined it that way'. 1+1=2 by definition as well. But that doesn't mean that definition always applies. People used to think negative numbers couldn't exist and that there was no such this as root-1. Definitions change.
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