1=.999999...?

[Terxpahseyton]

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.

The facts of football are objectively true you can't debate them. Everyone her in this thread who believes that football should be played with an egg is literally objectively wrong.

There is a way in which this analogy holds and a way in which it crutially fails.

Where it holds: Mathematics, in the strict sense of the word - that is academic Mathematics, is, as the rules football, a self-contained system, a tautology, and you can't debate a tautolgy. So far so good. Nothing special about Mathematics, but true in any case.
Where it fails: The standard to judge the rules of football depend on .. whim, really. So there is no basis to debate the rules unless one is agreed upon by whoever cares (not me). In the case of Mathematics, however, there is such a basis. Math is supposed to accurately represent the relation of quantities. Regardless of whether mathematics as they are established academically say that 1 = 0.99... one can question weather both numbers also are the same quantities. An angle which moves Mathematics right out of its self-rightious tautolgy and into a field of open debate.

And, btw, they are not That is really on the face of it. An infinite number has no pretension whatsoever of being an actual exact quantitiy. That should be really self-explanatory.

 

[Lohrenswald]

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.

what

 

[brennan]

What i'm trying to point out is that next week a conference of mathematicians could conceivably convene to address this question and decide to change the definitions that apply and so resolve the paradox in the opposite way. That 0.9999 =/= 1. This sort of thing actually happens in other fields you know. Pluto is a planet etc.

 

[Lohrenswald]

Actually, If they were to do that they would have to revoke a principle that sort of supports almost everything in mathematics (the completeness of numbers)

 

[brennan]

Have you heard of quantum mechanics? Physics chucked out all the fundamentals 100 years ago.

 

[Sonereal]

Have you heard of quantum mechanics? Physics chucked out all the fundamentals 100 years ago.

These are not at all similar sorry.

 

[Lohrenswald]

Have you heard of quantum mechanics? Physics chucked out all the fundamentals 100 years ago.

what

 

[NinjaCow64]

The facts of football are objectively true you can't debate them. Everyone her in this thread who believes that football should be played with an egg is literally objectively wrong.

If we define football as a game that should be played with a ball then yes, everyone here in this thread who believes that football should be played with an egg is literally objectively wrong. I've got to be honest, seeing the people who believe 1 =/= 0.999... playing football with an egg would be hilarious.

And I thought I was the one who made bad analogies Jesus.

There is a way in which this analogy holds and a way in which it crutially fails.

Where it holds: Mathematics, in the strict sense of the word - that is academic Mathematics, is, as the rules football, a self-contained system, a tautology, and you can't debate a tautolgy. So far so good. Nothing special about Mathematics, but true in any case.

lol what

Where it fails: The standard to judge the rules of football depend on .. whim, really. So there is no basis to debate the rules unless one is agreed upon by whoever cares (not me). In the case of Mathematics, however, there is such a basis. Math is supposed to accurately represent the relation of quantities. Regardless of whether mathematics as they are established academically say that 1 = 0.99... one can question weather both numbers also are the same quantities. An angle which moves Mathematics right out of its self-rightious tautolgy and into a field of open debate.

If you could actually find me 0.999... footballs, line them up and show me that they are different to a single football then I'd be really impressed. I'll give you Extra Credit for brining me a negative football, or an imaginary football.

And, btw, they are not That is really on the face of it. An infinite number has no pretension whatsoever of being an actual exact quantitiy. That should be really self-explanatory.

There is no nicer way of putting this: You are completely and utterly wrong. Why do you want to debate if you ignore every single piece of proof posted in this thread?

 

[Omega124]

Y'all need jesus Infinite Geometric Series.

I once had an issue explaining this concept to my AP Physics class. The Algebraic-based proofs feel like they should be wrong, even if they actually aren't. This proof doesn't rely on any algebra to make its proof, just one commonly accepted formula that you learn in Trig. Suddenly, my point came across. So, without further ado

If |r|<1, then ar+ar^2+ar^3...=(ar)/(1-r)

Let a=9 and r=.1

|.1|<1

.1<1

Therefore

ar+ar^2+ar^3...=(ar)/(1-r)

Now, focusing on the left equation first.

9*.1+9*(.1)^2+9*(.1)^3...

9*.1+9*.01+9*.001...

.9+.09+.009...

.999...

And then the right equation

(ar)/(1-r)

(9*.1)/(1-.1)

.9/.9

1

Altogether

.999...=9*.1+9*(.1)^2+9*(.1)^3...=(9*.1)/(1-.1)=1

 

[Sonereal]

That's like, just your opinion. Those numbers can change their definitions in a 100 years.

 

[Omega124]

That's like, just your opinion. Those numbers can change their definitions in a 100 years.

You know what definition doesn't change? RPG

 

[brennan]

https://en.m.wikipedia.org/wiki/Finitism

Interesting. Finitism, the rejection of the validity of infinite quantities and sets, has never been resolved and according to the incompleteness theorem cannot be proven incorrect.

 

[Omega124]

https://en.m.wikipedia.org/wiki/Finitism

Interesting. Finitism, the rejection of the validity of infinite quantities and sets, has never been resolved and according to the incompleteness theorem cannot be proven incorrect.

And these people still exist

That doesn't mean what they have to say is valid. Some people just want to watch the world burn be that guy.

 

[Sonereal]

You know what definition doesn't change? RPG

Interesting. Finitism, the rejection of the validity of infinite quantities and sets, has never been resolved and according to the incompleteness theorem cannot be proven incorrect.

Is this the hill you're willing to die on?

You can find a philosophy for literally anything.

 

[brennan]

And these people still exist

That doesn't mean what they have to say is valid. Some people just want to watch the world burn be that guy.

Heh. I've been active over on the flat Earth forum. I'm pretty sure none of them are serious but you'd be surprised how hard their 'official' thesis is to disprove.

Anyway. Sarcasm doesn't really undermine the fact that it appears that 0.999... =/= 1 is actually a perfectly valid position to hold.

 

[Omega124]

Heh. I've been active over on the flat Earth forum. I'm pretty sure none of them are serious but you'd be surprised how hard their 'official' thesis is to disprove.

Anyway. Sarcasm doesn't really undermine the fact that it appears that 0.999... =/= 1 is actually a perfectly valid position to hold.

It's only hard to disprove flat earth hypothesis if you slept through earth science.

It's not a valid position at all, though. A few cranks!=a valid mathematical theroy. Just like a few cranks!=a valid geological theroy. You can find any crackpot theory backed by a mathematician/scientist/historian simply because they want attention and have no sense of shame (Or, I guess they could also fail to grasp basic concepts in a field in which they dedicated their lives studying, which in some ways is even worse).

 

[brennan]

Let me make a proposal: let's introduce some new notation to the decimal representation of numbers.

Let 3 represent the rational number 0.01/3

1/3 can now be represented as 0.333

0.333... x 3 is still 0.999... but since 0.333... is no longer 1/3 then 0.999... =/= 1

 

[Omega124]

Let 3 represent the rational number 0.01/3

OK

Therefore, 3=.01/3=.00333...

1/3 can now be represented as 0.333

No. No it can't.

1/3=.333...

.33*.0033...=.0011

.0011!=.333.....

0.333... x 3 is still 0.999... but since 0.333... is no longer 1/3 then 0.999... =/= 1

1/3 is still .3333... You can't change values of pre-existing numbers without changing the base one uses (AKA, 6*9 actually does equal 42 when you use base 13).

EDIT: Furthermore, even if .333 DID equal 1/3, that still wouldn't change that 1/3=.333...

After all, (1/2)*(1/3)=1/6, but 1/6 still equals .1666... (Because, in fact, (1/2)*(1/3) ALSO equals .1666...)

 

[El_Machinae]

1/3 = 0.33 + 3-bar = 0.333...
1/3 x 3 = 0.99 + 0.01 = 1

 

[Sonereal]

1/3 = 0.33 + 3-bar = 0.333...
1/3 x 3 = 0.99 + 0.01 = 1

For the viewers in the audience, where does the .01 come from?