2=1.999...infinity! What are your thoughts?

[Josh]

Want to blow a child's mind?

Hold out your hands, fingers spread, and count the fingers on your left hand backwards from 10.

You will have: 10, 9, 8, 7 , 6. Emphasize the 6.

Then count the fingers on your right hand from 1:

1, 2, 3, 4 , 5.

Ask them what 5 + 6 is (11), and tell them you have 11 fingers.

Kids will think on that for an entire afternoon.

 

[Doctor Q]

Want to blow a child's mind?...

Warning! This trick will not work on kids who actually have 11 fingers. If only you had given me this warning in time! Now the little kid I tried it on at school is in the corner crying that I'm making fun of his abnormality and his mother is outside my house pounding on the door while his very large dad is trying to get in the window. And there is a live TV news crew waiting for me to come out and they stepped all over my flower garden. I'm going to try tunneling out of the house to escape.

I hope the rest of you won't share my fate. Count the kid's fingers before trying this trick!

 

[eva01]

Warning! This trick will not work on kids who actually have 11 fingers. If only you had given me this warning in time! Now the little kid I tried it on at school is in the corner crying that I'm making fun of his abnormality and his mother is outside my house pounding on the door while his very large dad is trying to get in the window. And there is a live TV news crew waiting for me to come out and they stepped all over my flower garden. I'm going to try tunneling out of the house to escape.

I hope the rest of you won't share my fate. Count the kid's fingers before trying this trick!

ok that was the best thing i have read all day, it has made me much happier still have a horrible headache but i am happier

 

[Flying Llama]

Warning! This trick will not work on kids who actually have 11 fingers. If only you had given me this warning in time! Now the little kid I tried it on at school is in the corner crying that I'm making fun of his abnormality and his mother is outside my house pounding on the door while his very large dad is trying to get in the window. And there is a live TV news crew waiting for me to come out and they stepped all over my flower garden. I'm going to try tunneling out of the house to escape.

I hope the rest of you won't share my fate. Count the kid's fingers before trying this trick!

HAHA! Man that was funny, that made my day!

llama

 

[diddy]

Lorenz added an infinite series of fractions in a similar method as the first poster. So from the point of view of classical mathematics, 2 is a correct value. But what do I know.

 

[jdechko]

That seems like some awfully generous rounding! 3.1415...all the way up to 10??? Hahaha.

That reminds me of the Simpsons episode where Lisa was explaining her nerd smell in front of the science committee and they all went crazy. Then the professor yelled "Pi is exactly 3!" and everyone freaked out.

In any case, I'll add my 1.999...infinity cents.... If someone gave me $2 billion (that is 2,000,000,000,000; my approximation of 2.0... infinity) and I only got $1,999,999,999,999 I would accept the "$2 billion" and not say a word about the missing fraction of a percent.

 

[bemylover]

$2 billion (that is 2,000,000,000,000;

that's 2,000,000,000 in fact. other than that I totally agree to your argument

 

[Anonymous Freak]

I was taught that it's true. (With links!)

In college Advanced Calculus (MTH 353, if I remember correctly,) our professor (a PhD in Mathematics from MIT, and a PhD in Theoretical Mathematics from CalTech,) showed us a proof that 0.999... is, indeed, exactly equal to 1. Yes, an actual proof. Sorry, it's been WAAAY too long for me to remember the proof. Not quite 1.999...=2, but mathematically similar. (I figure it has to hold true for all numbers that end in .999...)

Aha! My Google-fu is strong:
Wikipedia
Math Forum - Dr. Math
Descmath
Ask a Scientist at the Division of Educational Programs at Argonne National Laboratory

 

[gekko513]

that's 2,000,000,000 in fact. other than that I totally agree to your argument

On that note ... in English the number system goes like this:
thousand 1,000,
million 1,000,000,
billion 1,000,000,000,
trillion 1,000,000,000 ... right?

In norwegian it is ...
tusen 1 000,
million 1 000 000,
milliard 1 000 000 000,
billion 1 000 000 000 000,
billiard 1 000 000 000 000 000,
trillion 1 000 000 000 000 000 000,
trilliard 1 000 000 000 000 000 000 000 ... and so on

Why the difference? What do other languages use?

 

[Anonymous Freak]

On that note ... in English the number system goes like this:
thousand 1,000,
million 1,000,000,
billion 1,000,000,000,
trillion 1,000,000,000 ... right?

In norwegian it is ...
tusen 1 000,
million 1 000 000,
milliard 1 000 000 000,
billion 1 000 000 000 000,
billiard 1 000 000 000 000 000,
trillion 1 000 000 000 000 000 000,
trilliard 1 000 000 000 000 000 000 000 ... and so on

Why the difference? What do other languages use?

Even screwier, your 'English' units are only correct for American English. British English used to use slightly different units. (And some Britons still assume the old units, which are the same as your Norwegian above for milliard and billion.) The difference is properly called 'short scale' for the American versions, and 'long scale' for the former British system.

 

[bemylover]

all those terms come from one wod mille, which means thousand.

When Marco Pollo returned from China in 13th century, he was very impressed an tried to impress his fellow citizens by the wealths of China. The highest numbre expressed by one word was thousand(mille) at that time, which was not enough for him and that's when he invented a new one, million.

All these billions and trillions come from that million, so one should not look for a lot of meaning in those words.

 

[jdechko]

that's 2,000,000,000 in fact. other than that I totally agree to your argument

oops.

 

[obeygiant]

3 is a magic number!

 

[RHutch]

Unbelievable

I really can't believe how much discussion this topic got.

I am also surprised at some of the outrageous claims made (that 1.9999.... is an irrational number).

I will just add that all of the people who have said that 1.99999.... = 2 are correct. There are many ways to show this, and many have been stated in this thread.

Not that this will be any more likely to make the non-believers believe, but I do have a BS and MS in pure mathematics, and my thesis was in the area of infinite series.

 

[applebum]

Ok - after seeing this thread, all I really want to know is

when I purchase a song from iTunes for .99, am I really paying $1??? If so, where did my penny go??

I hate math!

 

[RHutch]

Ok - after seeing this thread, all I really want to know is

when I purchase a song from iTunes for .99, am I really paying $1??? If so, where did my penny go??

I hate math!

No. But if you purchase a song from iTunes for $0.999999999....., then you will be paying a dollar.

 

[Doctor Q]

Ok - after seeing this thread, all I really want to know is

when I purchase a song from iTunes for .99, am I really paying $1??? If so, where did my penny go??

The other penny goes to all the math geeks. We split it evenly amongst ourselves, using a very sharp chisel.

And now I'm sure this issue is settled.

 

[feakbeak]

People just need to become more knowledgeable about infinity.

Infinity is a difficult concept to wrap your head around. What do you think drove Cantor insane?

Another vote for 1.999... = 2 from another person with a math degree (BS in mathematics for secondary education).

As for those who have objections to infinity because it doesn't always have a practical purpose in engineering or in day-to-day tasks, you are missing the point. That is one of the beauties of mathematics, it not bounded by such practicalities.

For example, the importance of group theory was emphasized when some physicists using group theory predicted the existence of a particle that had never been observed before, and described the properties it should have. Later experiments proved that this particle really exists and has those properties.

Humanity learned a great deal about mathematics by making observations about the physical universe that we live in. Now, the tables have turned and we are understanding the nature of our physical universe by letting our minds run loose in the abstract world of mathematics. It's rather amazing if you think about it - reminds me of a quote by Einstein.

How can it be that mathematics, being after all a product of human thought, independent of experience, is so admirably adapted to the objects of reality?

 

[Iavhé]

It is true that 0.9 + 0.09 + 0.009 etc does equal 1. However the method in the original post for proving this is nonsense.

I do apologize though for assuming you were talking crazy talk. I'm a math major as well, and have often gotten into some interesting discussions when infinity came up.

Johnnowak,
I am currently in college, and I am going to MAJOR IN MATHEMATICS. I am really sorry to repeat myself, but BY DEFINITION: 1 is equal to .9999bar

Another vote for 1.999... = 2 from another person with a math degree (BS in mathematics for secondary education).

And now I'm sure this issue is settled.

I think not

I may not have a majore in mathematics but i still know 0.999...!=1

Lets say 0.999...=x

0.999...=(9/10)+(9/10^2)+...+(9/10^k)+...+(9/10^n)

0.999...*10=10x

0.999...*10=9+(9/10)+...+(9/10^k-1)+...+(9/10^n-1)

9x=(9+(9/10)+(9/10^2)+...+(9/10^k)+...+(9/10^n-1))-((9/10)+(9/10^2)+...+(9/10^k)+...+(9/10^n)) -->

9x=9-(9/10^n)

if 0.999...=1 shouldnt 9x=9 in this case? please proof me wrong

 

[atszyman]

if 0.999...=1 shouldnt 9x=9 in this case? please proof me wrong

You made the assumption of a finite sequence.

0.999...=(9/10)+(9/10^2)+...+(9/10^k)+...+(9/10^n)

should be

0.999...=(9/10)+(9/10^2)+...+(9/10^k)+...+(9/10^inf)

and

0.999...*10=9+(9/10)+...+(9/10^k-1)+...+(9/10^inf)

therefore

9x=(9+(9/10)+(9/10^2)+...+(9/10^k)+...+(9/10^inf))-((9/10)+(9/10^2)+...+(9/10^k)+...+(9/10^inf)) -->

9x=9

as described by Dr. Q's explanation of Aleph-0 earlier in this thread.

 

[eva01]

Surprised this popped up again. All you have to know is this

.1bar = 1/9
.2bar = 2/9
etc.
.8bar = 8/9

so

.9bar = 9/9 = 1

which will also work for 1 to 2

 

[monke]

Basically, this is the same as 1=.99999999

Two reasons:

.3333333333333333333333333333333333333333333333
times
3
equals
.9999999999999999999999999999999999999999999999

.3333333333333333333333333333333333333333333333
equals
(1/3)
times
3
equals
1

and this one:

1/3=0.33333.....
+2/3=0.66666.....
==============
3/3=0.99999.....=1

 

[Doctor Q]

At least we didn't spend 7 years finding a proof, announcing it, and then learning it was wrong. That's what happened to Andrew Wiles, who spent 7 years on a proof of Fermat's Last Theorem (which was not, in fact, Pierre de Fermat's last theorem). Wiles worked on his proof from 1986 to 1993 and then announced it to great fanfare. Soon after, a flaw it in was found. Luckily, he was able to work around the flaw and issue a corrected proof the next year.

Then there was the story of the mathematician from long ago who spent his entire career computing digits of pi, but made a mistake at one position, invalidating all of his remaining work. I couldn't find a reference to this story to find out any details. Perhaps somebody else knows.

 

[WildCowboy]

Then there was the story of the mathematician from long ago who spent his entire career computing digits of pi, but made a mistake at one position, invalidating all of his remaining work. I couldn't find a reference to this story to find out any details. Perhaps somebody else knows.

Ah yes...William Shanks.

 

[vniow]

Nerds.