1=.999999...?

[brennan]

How has this thread even reached page 15 when MadViking solved it in post 6???

Here's my even more simple formula:

1/3 = 0.3333333333... x 3 = 0.9999999999.

Hurr durr.

This proof is fallacious. Assuming that 1/3=0.333... is equivalent to assuming that 1=0.999... and thus is circular. That 1/3= 0.333... is open to question for exactly the same reason that 1=0.999... is. As I already pointed out, decimal cannot elegantly represent these numbers, which is what leads to the obvious problem that 1 appears to have two identities.

 

[Atticus]

Not elegant is different from incorrect.

That a number can be written in more than one way is no problem. 3/4 = 6/8 for example.

 

[Kyriakos]

Not elegant is different from incorrect.

That a number can be written in more than one way is no problem. 3/4 = 6/8 for example.

Yes, but that it can be written in more ways is also part of the axioms, albeit a very trivial axiom in this case (but axiom is from the greek Axioma, and from the term axiono, and literally means 'something aspiring to be taken as self-evidently true'-- the word alone means 'aspiration' with a cause, more or less).

The suspicion lingering here is that there are inconsistencies in the intermingling of axioms and their examination, in the specific case of 0.9999999... etc. I can't post more concrete stuff currently, though, cause i at least would need to have a look at how current algebra views numbers, and i likely will do so once i have more time (currently still looking for some more stable paid work...).

 

[Leifmk]

The suspicion lingering here is that there are inconsistencies in the intermingling of axioms and their examination, in the specific case of 0.9999999... etc.

No, there really isn't.

 

[Kyriakos]

No, there really isn't.

Even if indeed so, in the spirit of science one would have to look into this further (at least for one's own self, i plan to anyway, it is of interest).

 

[NinjaCow64]

Actually, 0.999... approximates 1. 1 is only equal to 1.

So yes, why is this even a thread?

No.

If you don't want to take it from the very knowledgeable people in this thread, at least take it from this educational video. It's a bit cutesy, but it's true.

https://www.khanacademy.org/math/recreational-math/vi-hart/infinity/v/9-999-reasons-that-999-1

 

[Tahuti]

This proof is fallacious. Assuming that 1/3=0.333... is equivalent to assuming that 1=0.999... and thus is circular. That 1/3= 0.333... is open to question for exactly the same reason that 1=0.999... is. As I already pointed out, decimal cannot elegantly represent these numbers, which is what leads to the obvious problem that 1 appears to have two identities.

It is not circular: What happens if you divide 1 by 3? Something you refer to as an just an 'assumption'.

 

[Leifmk]

Even if indeed so, in the spirit of science one would have to look into this further (at least for one's own self, i plan to anyway, it is of interest).

That is generally known as "studying mathematics", which is indeed a worthy pursuit and something that a few of us in this thread have already done.

 

[Kyriakos]

That is generally known as "studying mathematics", which is indeed a worthy pursuit and something that a few of us in this thread have already done.

Quite the self-assured sentiment coming from a barbarian of Oslo. My ancestors built mathematics, so by extension i am tied to them without needing to have a math degree. Every non-greek is a barbarian.
And return the nomismata paid to Harald Haldrada when he still was a captain in the Varangian Guard, Abel-kin norse-walker.

 

[Atticus]

^Kyriakos, I'm not sure what you are trying to say, but one source of confusion could be if you view axioms to be any evident truths. That is not the case. In maths the axioms are agreed upon. They are fixed. They don't have to be evident either. They can be completely wacky.

Of course, if you want to research things like distance or time, you want to use axioms that correspond to the intuition of those things, but that's a different thing. It is about usability of maths in physics etc.

Note also that the axioms of real numbers give names to only two numbers: 0 and 1. All the other names are there just out of convention. Especially you can't draw conclusion from them, for example that there can't be two different decimal names for the same real number (which I believe is the unconscious premiss of people arguing against this here).

EDIT: crosspost.

Again, there's no king's Greek's way to geometry.

 

[brennan]

It is not circular: What happens if you divide 1 by 3? Something you refer to as an just an 'assumption'.

If you divide 1 by three you get a third. I could turn the proof on it's head and say 0.333... =/= 1/3 since 3x0.333...=0.999... not 1

 

[Arakhor]

And that should tell you everything you need to know about the issue. It's really not quantum physics, you know.

 

[Akka]

I wonder why people with little or no actual education in mathematics keep believing they understand mathematics better than those who do have such education.

I also wonder if this phenomenon is as common in other fields of study. Probably is.

Oh yes it is. At least in the USA.
Look no further than "Creation vs Evolution" or "global warming is a lie" or other idiocies where fools brandish their ignorance as a proof that the facts are wrong.

 

[brennan]

Nor is it magnetism. What's the difference between magnetic field strength and magnetic flux density?:

 

[Mise]

Brennan, didn't you do a physics degree? I'm not saying that confers any special authority to Brennan over, say, Atticus or Leifmik (who, as I understand, are pure maths guys), but I don't think it's fair to accuse Brennan of ignorance or of lacking an education in maths. Formal, axiomatic maths, perhaps, but not the kind of maths that is motivating Brennan's arguments (which, incidentally, I don't buy at all).

 

[Akka]

It's just an approximation of a headache.

This is the most pigeon-chess thread I can remember since ever.

Pigeon-chess ?
I didn't knew the expression, but God yeah this is so fitting to this thread

How has this thread even reached page 15 when MadViking solved it in post 6???

Here's my even more simple formula:

1/3 = 0.3333333333... x 3 = 0.9999999999.

Hurr durr.

Nitpicking : you forgot the ellipsis at the end of the "0.9999999999.".

 

[Arakhor]

Nor is it magnetism. What's the difference between magnetic field strength and magnetic flux density?:

I haven't the foggiest idea, but I didn't do a physics degree. I just don't see it as worthwhile to worry about whether 0.3 recurring is not one-third, when there's far more difficult problems out there.

 

[brennan]

Magnetic field strength (H) is a vector quantity that tells you the magnitude and direction of the magnetic field. Magnetic flux density (B) is a vector quantity that tells you the magnitude and direction of the magnetic field. A conference decided at some point that these two identical things were different. Nobody seems to be able to explain why and most of the talk pages on wiki on the subject is various experts disagreeing vehemently about the matter. It seems to me that they could just as well have decided that they were exactly equivalent and done away with one (H most likely as it originated fron the notion of the field as originating from dipoles instead of current loops).

This seems to me to be equivalent to the arguments why 0.999...=1. Which seem dubious to me. If we met another ntelligent species I, as someone who knows a lot of physics would have absolutely no problem if they had decided that only one term for the magnetic field was necessary. What makes the mathematicians so positive they are absolutely correct about this 0.999=1 stuff?

At the moment we seem to be stuck with 'mathematicians agree about it'. Why? Who decided that 3x1/3=3x0.333...=0.999... therefore 0.999...=1 is true. When you could perfectly well say that 0.333...=/= 1/3 since 0.333...x3 =0.999... which =/= 1?

 

[Mise]

Yes well you can say a lot of things can't you.

 

[Borachio]

Pigeon-chess ?
I didn't knew the expression, but God yeah this is so fitting to this thread

Nitpicking : you forgot the ellipsis at the end of the "0.9999999999.".

"Pigeon-chess" is good. I like it a great deal, though I've never encountered it before either.

I fancy the reference is really to pigeon-chested, though.