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

[Doctor Q]

1/? approaches but never reaches 0 - its an infinitely small number...so, for standard math, you have to use the limit of 0 to solve the problem and have a usable answer.

If your solving proofs, you have forms for representing this, so I'd say 1.999...? ? 2, etc. in most other cases.

You are confusing two separate issues. The series 1.9, 1.99, 1.999, 1.9999, etc. does indeed approach 2 but never reach it. Its limit is 2 and its value isn't 2 because a series does not have a single value, just as the series 1/? approaches 0 but does not have a value.

But this is not the same thing as the number 1.999... (or written with .9 with a bar over the nine), which is one particular value that is indeed 2.

P.S. Typing & # 8 7 3 4 ; will get you a ∞ symbol.

 

[Loge]

Yes, 1.999999... and 2 are the same number. The difference between them is exactly zero. I also recall that every real number has a unique non-terminating decimal expansion; in this case the expansion of 2 is 1.999999.... Don't ask for proofs, it's too many years ago

 

[Hemingray]

Holy crap... I thought some of you guys were nuts until I saw the 1/3+2/3=3/3=1 so 1=0.999bar... now that's some crazy ****!

 

[adamcoop]

You may want to look at this, as it goes into some detail on the subject.
"Is 1 = 0.999....?"

 

[oldschool]

YOU'RE ALL NERDS!!!!!


(says he who just took a "break" from studying cell biology to read a macintosh computer rumors forum....)

 

[Roger1]

What this means is if I buy something for 1.99, you might as well say I bought something for 2.10. (allowing for 6% tax). But if I buy something for 2.00, then I might as well say I bought something for 2.12, allowing for tax. So if 1.99 =2.00, why does that extra .01 cost me an extra .02 when I buy something? After all, 1.99 equals 2.00, right???



edit: first/third person b/s

 

[Doctor Q]

YOU'RE ALL NERDS!!!!!

No, we all hate math and are in this thread because we all have the same homework problem and want somebody else to answer it for us.

Math joke: Did you hear about the race between two infinite sets? Aleph won!

 

[Counterfit]

and, of course, 12.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 (to infinity and beyond!)

You both forgot 00001101!!

 

[Counterfit]

And of course, the answer to this problem is 2 + 2 = 5











For very large values of 2.

 

[Doctor Q]

I had a computer science professor who said his office hours were "3pm plus epsilon to 4pm minus epsilon". That let him claim his office hours approached an hour, but still let him come in a bit late and/or leave a bit early, and then say "don't say I didn't warn you!"

 

[Santiago]

I just want to chime in to say that the mathematicians are right, and 1.9-repeating is an alternate representation of 2. It is only the case that sums over a finite number of terms of the series represented by 1.9-repeating approach 2; the sum of the infinite series is precisely 2. (The failure to understand this, or even the principle that an infinite series can have a well-defined finite sum, is what lead to one of Zeno's famous "paradoxes" regarding Achilles and the tortoise.)

 

[benbondu]

(The failure to understand this, or even the principle that an infinite series can have a well-defined finite sum, is what lead to one of Zeno's famous "paradoxes" regarding Achilles and the tortoise.)

After reading this whole thread, I think that pretty much sums it up. (no pun intended)

However, something that wasn't brought up: (this is for people who believe 1.9(bar) equals 2)

If 1.9(bar) and 2 are the same number and 2 is a member of the integers, is 1.9(bar) an integer?

I guess this is the same question as "is 2/2 an integer?"

 

[Santiago]

However, something that wasn't brought up: (this is for people who believe 1.9(bar) equals 2)

If 1.9(bar) and 2 are the same number and 2 is a member of the integers, is 1.9(bar) an integer?

Yes, in the same way that "two" is an integer. They are alternate notations for the same numerical value.

 

[Hemingray]

Math joke: Did you hear about the race between two infinite sets? Aleph won!

Naught again...

 

[pianojoe]

No way I'm going to read thru all this!

Please note:

1/9 = 0,1111.... periodic

therefore

9/9 = 0,9999.... periodic = 1,0000

q.e.d.

 

[PlaceofDis]

this thread has helped me appreciate all the books and all the criticisms i have read, all the papers i have written and all the discussions and lectures that i have sat through to become an English major, i cannot stand math, i am incapable of large math problems, Literature, writing, creative writing, thats what im good at

 

[Counterfit]

No way I'm going to read thru all this!

You should have because that was said at least three previous times.

 

[AmigoMac]

2 = 1.9999999 , it's great, it's a hope that we can be tolerant.

 

[billtanderson]

I look at this as a conversion problem.

Think of non-integer numbers as an analogue quantity. Our decimal number system is a digital representation of a number.

In some cases the representation can be exact, but it many it is just the nearest representation of the value. How close it is depends on the size of the quantization (I think thats the right word), or number of decimal places.


Take digital music, if we sample using 8 bits we get 256 discrete values to represent every possible value on the waveform, if we use 16 bits we get 65,636 etc. Thus the smaller the quantization (someone shout if this is the wrong word) the more accurately we can represent an analogue value with a digital number, but there are always infinitely more values in between each discrete one.

 

[King Cobra]

No way I'm going to read thru all this!

Heh, that's what I thought at first. (All right, who brought this thread back up from the dead anyways?)

Still, I think zapp's simple method/verification helps the most. (Though it also got the most controversy.)

Now, here's a riddle of a different sort: A mathematician and an engineer can't agree on the number of frames in a movie. If the movie is 2 hours long, then [A] how many frames are there according to both the mathematician and the engineer, whose answer is correct, and why?

Another question for the math majors right above.

 

[twenties1234]

it's true 1.999... ≡ 2

It's true 1.999... ≡ 2. The real numbers are complete and therefore have the betweenness property which states that between any two real numbers lies an infinite amount of real numbers. So, unless you can produce an infinite amount of numbers between 1.999... and 2, they must be the same number.

 

[Flying Llama]

Now i'm no pro in math, but from my simple logic, 1.999999999999999 is not the same thing as 2.0000000000000000. They are close, but not the same...

llama

 

[clayj]

I think it's pretty obvious that 2 != 1.99999999....9

If you assume the number of 9's in 1.99999999....9 is "x", then the difference between 2 and 1.99999999....9 is 0.["x-1" number of 0's]...1.

The difference maybe infinitely small, but it is a difference nonetheless.

 

[tobefirst ⚽️]

Was this thread *really* just drug up from a year ago so that it can be debated again???

 

[jsw]

The one thing I'm sure of is that the quantity (2 - 1.999...) is a precise measure of my concern for the correctness of any post in this thread.