I think there was already a thread (not on the brain teaser and puzzle forum) that had this question so if you saw the answer, please do not post it. Thanks.

Anyway, how is .999... equal to 1? It's actually simple, but a lot of people have a hard time figuring it out.

http://www.scienceforums.net/forums/showthread.php?t=17310

I've seen two proofs. One is the one where you try to change .99 repeating to a fraction and you end up with 1:

0.9999 repeating = x

9.9999 repeating = 10x

10x-x=9.9999... - 0.99999...

9x = 9

x=1!!

Also the easier one by far:

0.333333...+0.33333....+0.3333333...=0.99999....

0.3333....=1/3

1/3+1/3+1/3 = 1

Thus, 0.9999....=1

Alpha answered

 

http://antipsykopat.org/miniBB/index.php?action=vthread&forum=9&topic=12012&page=2

Okay, thanks. I didn't understand the first page of that thread, partly because it was in Norwegian.

Now to think about it, I didn't understand the 2nd, the 3rd and the 4th pages either. He seems to extremely anti-communism and curses Karl Marx wherever he can and seems to think that Marx had a diabolical plan to brainwash the entire earth population into believing 0.9 repeating equals 1.

He's not very satisfied with the proofs. Guess we'll never get the $50.000...

Is it $50.000 or $50,000?? *Drools*

 

Incidentally, you can ask him to write out a number between 0.999 repeating and 1 in decimal expansion form. But he will probably think of some highly intelligent answer to that as well.

1/9 = 0.1111111111111111...

2/9 = 0.2222222222222222...

3/9 = 0.3333333333333333...

4/9 = 0.4444444444444444...

5/9 = 0.5555555555555555...

6/9 = 0.6666666666666666...

7/9 = 0.7777777777777777...

8/9 = 0.8888888888888888...

9/9 = 0.9999999999999999...

 

 

0.9999999999... is a rational number just like all the others, and I dont know how else to write its fraction equivalent except as 9/9, which is 1. So .9999999999... = 1.

 

What could be more straightforward than that?

also... it is true that for every number that is not equal, there is a number between it and ANY other number...

 

If .9999999999...?1, then .99999999......+x<1. so... after careful thought, realizing that you have an infinite number of nines... if you add ANY number, (unless you have an infinite number of zeros with a one after it... which is not possible), you get a number greater than one... for instance... you add .000000001 and you get 1.00000000099999999999999999....... and so on... Therefore .99999....=1, because there is no number between .99999... and 1.

Okay' date=' thanks. I didn't understand the first page of that thread, partly because it was in Norwegian.

Now to think about it, I didn't understand the 2nd, the 3rd and the 4th pages either. He seems to extremely anti-communism and curses Karl Marx wherever he can and seems to think that Marx had a diabolical plan to brainwash the entire earth population into believing 0.9 repeating equals 1.[/quote']

 

This has to be the strangest thing I've ever seen in any of the many rediculous threads on this subject. It makes me wish I spoke Norwegian so I could understand the rest of his clearly original material.

As I said many times, don't ask me to ask Alpha for you, ask him yourself. I've given url to where you'll find him. Even though most of what's on that forum is in Norwegian he will answer you in English. If you meet a Norwegian who doesn't understand English he has either skipped school or slept in classes

Feel free to ask Alpha about anything as long as it's relevant.

Okay, thanks. I didn't understand the first page of that thread, partly because it was in Norwegian.

You're not going to understand it, even if it were in English, because it's nonsense. In the world of math cranks, the 0.99_ is not 1 people outnumber the circle quadrature cranks by exactly 314,159 to 1, and there's no shortage of absurd reasoning ranging from "limits are nonsense, we should use infinitesimals" to "Zeno was right about his paradoxes, there is no motion."

 

Now to think about it, I didn't understand the 2nd, the 3rd and the 4th pages either. He seems to extremely anti-communism and curses Karl Marx wherever he can and seems to think that Marx had a diabolical plan to brainwash the entire earth population into believing 0.9 repeating equals 1.

My favorite part was when he whined about Ayn Rand failing to make an appearance in the Stanford Encyclopedia of Philosophy, and cited that as proof of an academic conspiracy against the Truth™. Funny how crankdom and conspiratorial thinking go hand-in-hand.

 

He's not very satisfied with the proofs. Guess we'll never get the $50.000...

Is it $50.000 or $50' date='000?? *Drools*[/quote'] As I mentioned in Trond's other thread, some European countries use a "," where we would use a "." So it's fifty-thousand dollars.

 

Incidentally, you can ask him to write out a number between 0.999 repeating and 1 in decimal expansion form. But he will probably think of some highly intelligent answer to that as well.

Well, not so much a highly intelligent answer as a clever dodge.

"My favorite part was when he whined about Ayn Rand failing to make an appearance in the Stanford Encyclopedia of Philosophy, and cited that as proof of an academic conspiracy against the Truth™. Funny how crankdom and conspiratorial thinking go hand-in-hand."

 

And what's funny now is that you don't know why

And what's funny now is that you don't know why

I don't? That's news to me.

I don't? That's news to me.

You don't really have any interest in this.

 

Or

 

Why don't you ask Alpha (Norway's most rational philosopher?) why he makes those statements. Feel free to take an intellectal combat so everyone can see that Alpha is really wrong

Why don't you ask Alpha (Norway's most rational philosopher?) why he makes those statements. Feel free to take an intellectal combat so everyone can see that Alpha is really wrong

Sorry, I've contributed more than my fair share of arguing this point, and would rather not continue with someone who insists all arithmetic must be numerical (such that an objection like "you can't keep adding 9s infinitely" might hold water) as opposed to analytic (where such an objection holds none). All his yacking about Marx, Newton, feminists and political correctness doesn't do much to help convince me he has all his marbles. Also, I'm not sure how to interpret your claim that he is Norway's most rational philosopher as anything but an ethnic slur against the good people of Norway.

Well you did your best, chickened out and gave up.

because there is no number between .99999... and 1.

There is a number between .999999 and 1. It's .9999992, no?

But that isn't between 0.99... and 1 and has nothing to do with anything. Stop the necrophilia.

1/9 = 0.1111111111111111...

2/9 = 0.2222222222222222...

3/9 = 0.3333333333333333...

4/9 = 0.4444444444444444...

5/9 = 0.5555555555555555...

6/9 = 0.6666666666666666...

7/9 = 0.7777777777777777...

8/9 = 0.8888888888888888...

9/9 = 0.9999999999999999...

 

 

0.9999999999... is a rational number just like all the others' date=' and I dont know how else to write its fraction equivalent except as 9/9, which is 1. So .9999999999... = 1.

 

What could be more straightforward than that?[/quote']

 

9/9=1, it is not 0.9 recurring, what could be more straight forward than that, I don't recall anyone talking about significant numbers. What do you mean by rational ? What equation comes up with .9 recurring out of interest ?

If you follow the pattern it would seem that .9 repeating is the same as 1. She's not talking sig digits, this is one way to show that 1 seems to be the same as .9 repeating.

The sequence stops as soon as you divide the figure by itself...0.9 recurring has nothing to do with 1, unless I'm completely off the mark...I'm currently studying this, so please explain how the sequence works, unless you're rounding off 0.9 recurring how can it equal 1 ?

I think it's just one theory. There's a lot of grey area as to what it means.

There's a lot of grey area as to what it means.

 

Thanks Juststuit...I thought I was missing something obvious for a second.

Mathematically, .9 repeating and 1 represent the same idea (ie. they are the same number). 1/3 represents the same idea as .3 repeating. 1/3 + 1/3 + 1/3 is 1. .333_ + .333_ + .333_ = .999_ Since 1/3 and .333_ are equal (they portray the exact same value) then .333_ + .333_ + .333_ = 1/3 + 1/3 + 1/3 and thus .999_ = 1. No rounding is being done here. .999_ and 1 represent the same concept.

Snail, JustStuit, stop it. There is no grey area, there are no competing thoeries. 0.99... and 1 are different representations of the same number, just like 1/2, 2/4, 3/6, and 1234/2468 are all different representations of the same number.

 

The Real Numbers, the place where this argument takes place, are a complete metric space, 0.99... is the limit of the sum

 

S(n)=9/10+9/100+...+9/10^n

 

and lim S(n) as n tends to infinity is 1. That is easy to prove since the distance between S(n) and 1 is 1/10^n and this converges to zero. Since limits are unique this shows that these two symbols represent the same number.

Snail, JustStuit, stop it.

 

Understood, I think I'll be avoiding the maths sections until I've finished my course...I'm clearly not competent enough to be posting in these areas.

 

Apologies to IMM for being my usual rash self.