Is 1 = 0.9999......

[spanky]

i always leave a machine after i win. i never won anything big tho... usually just like $5, $10, or $20. most i ever won from slots was $75. i never expect to hit the big one (tho it would be nice)... but after i get some... i'm outta there full throttle

 

[bleeb]

First time I hit the slots, just after I turned 21, I won $250 Bones!!

 

[Yax]

Originally posted by: bleeb
First time I hit the slots, just after I turned 21, I won $250 Bones!!

Probably no one will read this thread this far, unless they skip to the end. 0.9...=1 is correct. Anyone who argues otherwise never got an A above basic Algebra. If they did, then their teacher was wrong or too lazy to give them a proper grade.

 

[DrPizza]

I've noticed quite a few professions that I'm impressed with in here... (wow, nuclear physicist in the bunch!)
Nonetheless, no matter how smart you are, unless you've got the background in this type of mathematics, you're not qualified to answer definitively. I can't believe this thread is going on soooo long! So, why doesn't everyone take real analysis (an upper level math class). Once everyone does, you can do a really rigorous proof and you'll all realize that .99999repeating does indeed equal 1. Then again, no matter how much proof you give someone, some people absolutely refuse to change their minds and insist they've been correct from the start... I read a bunch of various "proofs" that they aren't equal... each of those proofs was shot down. But, no one has correctly shot down the proofs that they are equal.

 

[GambiT]

Here's my contribution to this long debated issue:

Fact:
1/9 = .11111111...
2/9 = .22222222...
3/9 = .33333333...
...
8/9 = .88888888...
9/9 = .99999999...

9/9 = 1

 

[MadRat]

Originally posted by: cheapbidder01
Anyone who argues otherwise never got an A above basic Algebra. If they did, then their teacher was wrong or too lazy to give them a proper grade.

Another assumption that is plain wrong. Just because a person doesn't become a math major doesn't mean squat about their comprehension of math. Interesting that you'd introduce the idea of "grades" as being proper one way or another. Reminds me of the debate about percentiles for grades as opposed to pass/fail. I've seen plenty of students with grade point averages above 100%, from deans nonetheless, so does that make professors that refuse higher scores that 100% any less elite?

 

[MadRat]

Originally posted by: GambiT
Here's my contribution to this long debated issue:

Fact:
1/9 = .11111111...
2/9 = .22222222...
3/9 = .33333333...
...
8/9 = .88888888...
9/9 = .99999999...

9/9 = 1

9/9 <> .99999999...

 

[vtqanh]

Originally posted by: GambiT
Here's my contribution to this long debated issue:

Fact:
1/9 = .11111111...
2/9 = .22222222...
3/9 = .33333333...
...
8/9 = .88888888...
9/9 = .99999999...

9/9 = 1

Even though i agree that 1 = 0.9999, but your proof is wrong. 9/9 = 0.99999999 is not a fact.

 

[josphII]

Originally posted by: vtqanh

Originally posted by: GambiT
Here's my contribution to this long debated issue:

Fact:
1/9 = .11111111...
2/9 = .22222222...
3/9 = .33333333...
...
8/9 = .88888888...
9/9 = .99999999...

9/9 = 1

Even though i agree that 1 = 0.9999, but your proof is wrong. 9/9 = 0.99999999 is not a fact.

actually it is, he just didnt prove it

 

[Kyteland]

Folks, we need a new math thread to argue about, and it looks like this is it! Have fun.

http://forums.anandtech.com/messageview.cfm?catid=38&threadid=1062959

 

[MadRat]

In base 10 the result of 9/9 is 1. No .999.... involved. To prove .999...=1 would require breaking the distinction between the abstract and the rational worlds. Like its been explained over and over, infinity and null are values not represented in the natural world. We use them for math to define ideals that do not exist. Ideals by the definition do not exist. The number .999... does not exist but we can theorize about it if we use ideal terms. Rationally all numbers would be a distinct fraction of the whole. In philosophy the very presence of "one" as a value can be either abstract or rational. In one instance it may include one part of a whole while in another it includes everything. Depending on its use defines whether it is being used abstratly or rationally. The gist of the whole argument is that some people believe ideally that .999... is equal to one. The majority here believe that ideally .999... and 1 are distinctively different. The ideals and rationalizations do not exist together so neither answer is either correct or wrong.

 

[Hector13]

Originally posted by: MadRat

Originally posted by: GambiT
Here's my contribution to this long debated issue:

Fact:
1/9 = .11111111...
2/9 = .22222222...
3/9 = .33333333...
...
8/9 = .88888888...
9/9 = .99999999...

9/9 = 1

9/9 <> .99999999...

I haven't bothered reading this whole thread, but I do remember this topic comming up before when the "highly technical" forum was created. Sadly, I also remember that no matter how many valid, mathematical proofs were give, madrat (and a couple others, I believe) would not accept that .9999r = 1. This topic is exactly like the one on "probability" a couple days ago. Some people will just "see" the anwser, and a bunch won't.

Those of you who don't' agree here need to realize that our number system is an "invention" (not some universal, god-given thing). They way it is established requires that .999r = 1. If you want to read this from a "real" mathematician, I suggest you get the book Infinity and Beyond it should help you clear up this and any other misconceptions you might have about our number system.

 

[Hector13]

Originally posted by: silverpig

Originally posted by: Acanthus
i can apply the same logic the .99999r people are using to any number and round it to whatever i want.

.9r does not = 1

no book can prove or disprove that, its the holy grail of math

No you can't. 3 != 5 because 4 is > 3 and < 5. Therefore 3 < 5.

You can't find any such number in between 0.9... and 1.

And even if you could find a number between .99r and 1 (let call it "x"), what whould x*10 be? x*10? How about x * 1000000000000? And then what would 1 - x be?

 

[MadRat]

There is no mathematical principle that requires .999... to equal 1, Hector. That is a claim that has no substantiation.

 

[josphII]

Originally posted by: MadRat
There is no mathematical principle that requires .999... to equal 1, Hector. That is a claim that has no substantiation.

yes there is, its called the principles of addition, subtraction, multiplication, and divistion - the basis for every mathematical function including every expression in the proof of 0.999... = 1

 

[FrustratedUser]

I am sceptic,

 

[CrazyPerson]

i drink to that :beer:

 

[bleeb]

Originally posted by: CrazyPerson
i drink to that :beer:

0.9999... != 1. Just thought I'd throw that in for old times sake.

 

[ndee]

so 1.99999999999999999999999999999999999... = 2?

 

[Hector13]

Originally posted by: MadRat
There is no mathematical principle that requires .999... to equal 1, Hector. That is a claim that has no substantiation.

madrat, if you don't like the rules and axioms that our number system is based on, then fine, don't use it. Make up your own crap where 1=2 for all I care.

If, however, you use our number system, then you have to accept all its axioms and principles. In the number system defined by these axioms, .9999r = 1. If you can't comprehend that, then that is your problem. Being ignorant of the fundations of our number system pretty much means your opinions about it are worthless.

 

[CrazyPerson]

1~.09999999999...
they are so close... therefore .9999999=1

 

[Eli]

This thread is like the Energizer bunny.

 

[AmbitV]

Well of course .999... and 1 are not the same. Just like Joseph and Joe are not the same. But Joseph and Joe refer to the same person. Similarly, .999... and 1 refer to the same thing. Oh wait, what is this "thing". Hmm, guess it's a concept. Can there be a concept of a number, or are numbers concepts?

 

[RossGr]

Another assumption that is plain wrong. Just because a person doesn't become a math major doesn't mean squat about their comprehension of math.

There is no mathematical principle that requires .999... to equal 1, Hector. That is a claim that has no substantiation.

These 2 comments of Matrats demonstrate much of what is happening in the world today. Every yahoo with a deeply held belief feels that that belief makes him an expert. How can you make that last statement? Does your deeply held belief equal fact? I think not.

As was stated above the equality of 1 and .999... is a feature of the contstruction we call the Real number system. Mathematicans spend a lot of time learning the foundations of this system it forms a basis for mush of mathematics.

You need to realize that your nonmathematical world view is not the only or necessarily correct world view. Unfortunatly your belief system interfers with your ability to learn.

 

[RossGr]

Originally posted by: vman
Well of course .999 and 1 are not the same. Just like Joseph and Joe are not the same. But Joseph and Joe refer to the same person. Similarly, .999 and 1 refer to the same thing. Oh wait, what is this "thing". Hmm, guess it's a concept. Can there be a concept of a number, or are numbers concepts?

you are quite right .999 <> 1 but also .999 <> .999...

Those 3 little dots make a lot of difference.