0.9999999999.... vs 1?

[Ozymandyus]

I'm confused. Are we saying that it's fun to make up proofs that LOOK like .9r is the same as 1, or are we saying that they are ACTUALLY the same number? I guess i'm interested if it's ACTUALLY the same number, but the proof i read earlier just looks like one of those algebra paradox things I get in my spam mail.

No we are saying that they are ACTUALLY the same number.

The problem is that we cannot properly understand infinities, as shown by the only attempted anti-proof earlier which referred to '0.0 repeating infinitely with a 1 perched on the end' which is a completely meaningless concept. 0.9 repeating is 1. Exactly 1. Think of it as just another way of writing it, like writing 1/1 or 15/15 or 0.5x2. The decimal system is defined this way, and it is just our poor understanding of infinity that seems to draw a distinction between the numbers 1 and 0.9(9)...

There is no such thing as a true paradox in math, only poorly dealt with concepts of infinity and mistakes in human calculation. Irrational numbers like pi and e are very difficult to deal with, and of course imaginary numbers like the square root of -1 can be used to give the appearance of a paradox, but math has real defintions of those numbers and can deal with them if you follow the rules. Any apparent paradoxes are not truly there, as the entire system of math is a tautological construct - you cannot prove anything using math that disproves it, because it is defined to be whole-ly true.

 

[felixthecoach]

Ah, well then. This thred is now interesting to me.

 

[Josan]

could be but for all intentive purposes it is correct even in rocket science they only work to three decimal places so the point is mute

It is correct, and we know that it is correct. And while you are correct in stating that in practical use the point is moot, it is still a very interesting question for anyone with any slight interest in math. Math doesn't opperate on what might be usefull, it opperates on what it can actually proove, and this is a good thing, our mathematic knowledge has come far.

I'm confused. Are we saying that it's fun to make up proofs that LOOK like .9r is the same as 1, or are we saying that they are ACTUALLY the same number? I guess i'm interested if it's ACTUALLY the same number, but the proof i read earlier just looks like one of those algebra paradox things I get in my spam mail.

As Ozymandyus pointed out, we are saying that they are the EXACT same number, and we can proove it. The spam are false prooves because they break simple rules within mathematics, we discussed this earlier in the thread.

what i am saying is that we will never know

I am sorry, but you are wrong, we can know, and we DO know.

I think it was a bad idea to have a poll about this, this is like having a poll about "Is evolution real?". People are wrong and vote wrong, it still doesn't make it right. I am sorry if I offend someone. And if you really need any more persuasion, a good place to start could be the wikipedia article about this exact topic.

11 people voting "definitly no", sheesh.

 

[Ozymandyus]

Yeah, the 11 people voting definitely no was what shocked the hell out of me. It's like believing the sun spins around the earth to me. Sure, it is not immediately obvious, but we assume that the people that know math and science are not misleading us.

The big problem is so many people find math so boring that they don't know AND they don't care.

 

[felixthecoach]

LOL how are you guys shocked? The poll is set to up for anybody, even if they don't have a working knowledge of complex math theories (ehem, Felixthecoach)

Second, the poll question reads like this,

"Are they the same number?"

Well, to the untrained eye (again, Felixthecoach) it looks iike the number .999 and the number 1 are different from each other. I know a little about calculus and Limit equations, but I assumed they never actually touched, just kept getting closer until it was negligible.

Sorry, it just makes me laugh that people are like, "OMG did you see how many people voted NO?"

But whatever, you guys are right, .9r is a cool way of saying 1.

Question, if i was speaking in binary and wanted to express .9r to my fellow computer geek, what would I type? :lol:

 

[Josan]

Why I am shocked? Because this is a continiued thread from the earlier forum, so I imagine most of those who vote has actually read that topic including proofs. And I would assume that if there was a factual question that only those who were actually quite certain of themselves would vote, and at least read the thread devoted to the problem before making up their mind. And if there had been 11 people vointing "maybe not, I'm not sure" or 8 people voting "I have no idea", then I wouldn't have been shocked, but no... 11 people on this forum are absoloutly certain that 0,999... does not equal 1, and that is what I find shocking.

And sorry, I can't help you, I suck at binary

 

[felixthecoach]

Well, if it makes you feel any better. I'd change my vote now that I know. But for some reason this thread is set up like an election, I only vote once and I wasted it on Nader this time around...Sorry.

(FTR I voted obama, but that's another thread)

 

[Ozymandyus]

I was just surprised as it strikes me as a common knowledge thing... Like when I first found out that a bunch of people don't believe in evolution, I was shocked as hell. As I mentioned, the real problem is that math in general is presented as so boring that no one is really interested in these sorts of questions...

We all know that the earth revolves around the sun even though its not readily apparent and has no affect on our daily lives... because its cool as hell. We are hurtling through space at hundreds of thousands of miles per hour. Awesome. I find the concept of infinity in math equally awesome, but I don't think it is presented to people correctly.

 

[Pulsar]

Question, if i was speaking in binary and wanted to express .9r to my fellow computer geek, what would I type? :lol:

That would be 0.111111... = 1.
If you like a proof, here's a way to do it:

1/3 = 1/4 + 1/12
= 1/4 + 1/16 + 1/48
= 1/4 + 1/16 + 1/64 + ...
= 2^(-2) + 2^(-4) + 2^(-6) + ...

So, in binary notation, we have
1/3 = 0.01010101...
2/3 = 0.010101... + 0.010101... = 0.101010...
3/3 = 0.010101... + 0.101010... = 0.111111... = 1

QED

It works in any base. For instance, in base 3, it follows that 0.2222... = 1.

 

[felixthecoach]

*AHHHHHHHHHHHH*

BAM

Blood begins to spit out of the top of the neck, arms go limp, knees buckle, and a baby begins to cry...

 

[Aught3]

@Felix
They're the same number, nobody is trying to trick anyone else.

I had another thought about why 0.(9)=1 might be so hard to understand. It's because we're used to thinking that one numerical 'value' can only be represented by one number. 1=1, 2=2, etc. Maybe it will help to realise that it's not only the value 1 that can be written in two ways [1 & 0.(9)] but every value can be represented by two numbers.

2=1.999...
3=2.999...
24.57=24.56999...

And so on.

 

[felixthecoach]

Okay, well i believe you. Guess it's like the concept that the universe size is infinite. I just cant picture that.

 

[Master_Ghost_Knight]

Okay, well i believe you. Guess it's like the concept that the universe size is infinite. I just cant picture that.

Actualy nobody claims that the universe is infinite, altough in pratical terms because of the light cone, it is to you, but that is a story for a physics thread (for which this particular topic is not my strong point).

 

[felixthecoach]

Actualy nobody claims that the universe is infinite

Fuck....


I'm just gonna stick to psychology.

 

[Master_Ghost_Knight]

Advanced physics and math is great, it is just invariably very counter-intuitive.

But sometimes elegant answers and extreme coincidences do arise in unexpectade places, and that is the buty of it.

 

[Th1sWasATriumph]

My thinking is still primitive: 0.999999999999 . . . is not 1, because it . . . just isn't?

If you have a formula that results in 1, and a formula that results in 0.99999999999999..., how could you call them the same number? It's a difference in value.

Yes yes, I'm aware of all the "proof", but you can prove anything with numbers.

 

[Aught3]

^Surely that post merits a loss of moderator privileges :lol:

 

[Josan]

If you have a formula that results in 1, and a formula that results in 0.99999999999999..., how could you call them the same number?

I am not sure what you mean, if you could ellaborate further.

It's a difference in value.

By how much?

Yes yes, I'm aware of all the "proof", but you can prove anything with numbers.

You can only proove that which is true based on your axioms. Proof in math is proof indeed...

 

[blinddesign]

Question, if i was speaking in binary and wanted to express .9r to my fellow computer geek, what would I type? :lol:

that reminds me- i need to start a binary help/discussion thread. i get the concept but i need help with 'advanced' binary like how to write stuff after the decimal (or binary?) point.

 

[Ozymandyus]

Yes yes, I'm aware of all the "proof", but you can prove anything with numbers.

This is something that a lot of people seem to think around here. It's not true.

If anyone would please feel free to try to post any proofs of things that are clearly not true, and I'm quite sure someone here can tell you what someone did wrong in it. Math is constructed to be absolutely true - you can't prove anything with math that is not absolutely true. Applying it to the world can lead to apparent contradictions, though often not really.