Wow I bet my comp sci PHD room mate 100 bucks that 0.9999.. = 1

[mjrpes3]

http://arxiv.org/PS_cache/arxi...f/0811/0811.0164v8.pdf

In the matter of teaching decimal notation, we would like to obtain
some reaction from educators to the following proposal concerning the
problem of the unital evaluation of .999 . . .. A student may ask:
What does the teacher mean to happen exactly after
nine, nine, nine when he writes dot, dot, dot?
How is a teacher to handle such a question? Experience shows that
toeing the standard line on the unital evaluation of .999 . . . possesses
a high-frustration factor in the classroom. Rather than ba?ing the
student with such a categorical claim, a teacher could proceed by pre-
senting the following ten points, based on the material outlined in
Section 11:
(1) the reals are not, as the rationals are not, the maximal number
system;
(2) there exist larger number systems, containing in?nitesimals;
(3) in such larger systems, the interval [0, 1] contains many numbers
in?nitely close to 1;
(4) in a particular larger system called the hyperreal numbers, there
is a generalized notion of decimal expansion for such numbers,
starting in each case with an unbounded number of digits ?9?;
(5) all such numbers therefore have an arguable claim to the no-
tation ?.999 . . .? which is patently ambiguous (the meaning of
the ellipsis ?. . .? requires disambiguation);
(6) all but one of them are strictly smaller than 1;
(7) the convention adopted by most professional mathematicians
is to interpret the symbol ?.999 . . .? as referring to the largest
such number, namely 1 itself;
(8) thus, the students? intuition that .999 . . . falls just short of 1
can be justi?ed in a mathematically rigorous fashion;
(9) the said extended number system is mostly relevant in in?nites-
imal calculus (also known as di?erential and integral calculus);
(10) if you would like to learn more about the hyperreals, go to your
teacher so he can give you further references.

 

[silverpig]

Originally posted by: mjrpes3
http://arxiv.org/PS_cache/arxi...f/0811/0811.0164v8.pdf

In the matter of teaching decimal notation, we would like to obtain
some reaction from educators to the following proposal concerning the
problem of the unital evaluation of .999 . . .. A student may ask:
What does the teacher mean to happen exactly after
nine, nine, nine when he writes dot, dot, dot?
How is a teacher to handle such a question? Experience shows that
toeing the standard line on the unital evaluation of .999 . . . possesses
a high-frustration factor in the classroom. Rather than ba?ing the
student with such a categorical claim, a teacher could proceed by pre-
senting the following ten points, based on the material outlined in
Section 11:
(1) the reals are not, as the rationals are not, the maximal number
system;
(2) there exist larger number systems, containing in?nitesimals;
(3) in such larger systems, the interval [0, 1] contains many numbers
in?nitely close to 1;
(4) in a particular larger system called the hyperreal numbers, there
is a generalized notion of decimal expansion for such numbers,
starting in each case with an unbounded number of digits ?9?;
(5) all such numbers therefore have an arguable claim to the no-
tation ?.999 . . .? which is patently ambiguous (the meaning of
the ellipsis ?. . .? requires disambiguation);
(6) all but one of them are strictly smaller than 1;
(7) the convention adopted by most professional mathematicians
is to interpret the symbol ?.999 . . .? as referring to the largest
such number, namely 1 itself;
(8) thus, the students? intuition that .999 . . . falls just short of 1
can be justi?ed in a mathematically rigorous fashion;
(9) the said extended number system is mostly relevant in in?nites-
imal calculus (also known as di?erential and integral calculus);
(10) if you would like to learn more about the hyperreals, go to your
teacher so he can give you further references.

ANYONE can post something on the archive.

 

[Chris27]

a - b == 0 if and only if a == b
0 == 0.0... by how we define the decimal representation of the real numbers
1 - 0.9... == 0.0... (There is no "1" as we are dealing with an infinite stream of zeros. If there existed a 1 at the "end", the existence of an "end" contradicts the statement that 0.9... is an infinite steam of 9's)
1 - 0.9... == 0
1 == 0.9...
Q.E.D
can this thread end now?

 

[GodlessAstronomer]

Originally posted by: Chris27
a - b == 0 if and only if a == b
0 == 0.0... by how we define the decimal representation of the real numbers
1 - 0.9... == 0.0... (There is no "1" as we are dealing with an infinite stream of zeros. If there existed a 1 at the "end", the existence of an "end" contradicts the statement that 0.9... is an infinite steam of 9's)
1 - 0.9... == 0
1 == 0.9...
Q.E.D
can this thread end now?

Get back in your cave, lurker :|

 

[halik]

Originally posted by: PlasmaBomb

Originally posted by: SSSnail

Originally posted by: arcenite

Originally posted by: SSSnail

Originally posted by: arcenite

Originally posted by: SSSnail

Originally posted by: PlasmaBomb

Originally posted by: SSSnail
Blame it on our flawed arithmetic, while 1/3 + 1/3 + 1/3 does equal 1, 1 divide by 3 does not compute in terms of infinite. I understand perfectly the problems and your answer, and why the proponents for .9999.... = 1 have the proof with the current laws of calculation. All I'm saying is, look at it differently from an infinite point of view, and you'll have a problem.

Please solve 1/3 as a decimal to its maximum finite length. You are not allowed to post again until you do.


*wave*

You do the same... 😕

It can't be done. You are saying that it can.

It's not, I'm saying that it can't because it doesn't compute. You guys are the ones saying it can because you magically stopped .9999.... somewhere for it to be 1.

NO.

.99... does not stop. Ever.

But 1 does, now there's something for you to think about.

/Facepalm

Wow...

 

[Born2bwire]

Originally posted by: halik

Originally posted by: PlasmaBomb

Originally posted by: SSSnail

Originally posted by: arcenite
NO.

.99... does not stop. Ever.

But 1 does, now there's something for you to think about.

/Facepalm

Wow...

Look what you've done halik. Look at this! What did ATOT ever do to you, huh? What did we do to deserve this plague?

You're a bad man halik, a very very bad man.

 

[SagaLore]

Originally posted by: SlitheryDee
x= .999...

10x = 9.999...

10x - x = 9.999... - .999...

9x = 9

x = 1

x = .888...

10x = 8.888...

10x - x = 8.888... - .888...

9x = 8

x = 8/9 = .888...

Okay I'm convinced. 🙂 This is why:

1/1 = 1.000000...
1/2 = 0.500000...
1/3 = 0.333333...
1/4 = 0.250000...
1/5 = 0.200000...
1/6 = 0.166666...
1/7 = 0.142857... (weird one)
1/8 = 0.125000...
1/9 = 0.111111...
2/9 = 0.222222...
3/9 = 0.333333...
4/9 = 0.444444...
5/9 = 0.555555...
6/9 = 0.666666...
7/9 = 0.777777...
8/9 = 0.888888...
9/9 = 1.000000...

If you treat the repeating zeroes the same, you can see that 0.999... really is an alternative way of representing 1, but its only one way. You have to remove the idea that it goes on infinitely in reality, but rather just on paper.

So 1.000... = 0.999..., but you can't calculate anything with it properly because its just a representation/result.

 

[OCGuy]

I just put it in my calculator, and it confirmed that indeed 1=1.

This in fact proves that .99999.... = .99999......

 

[her209]

I made this for you guys.
http://pics.bbzzdd.com/users/h...9/Philosoraptor999.jpg

 

[Atomic Playboy]

Originally posted by: SSSnail
So, .0000......1 x infinity is NOT 0. Which is it? You can't have both, either you're talking about infinite or a finite number. As soon as you stop anywhere on the .9999.... I'll have a .0000...1; if we're talking about infinite, then see above.

I think I just broke your .9999.... = 1.

Give the man his money.

0.000...1 is not a number. It's not possible. Let's explore why.

For the sake of this discussion, let's replace the word "infinite" with the word "endless." I think we can agree they are synonymous; if you can't accept that, Merriam-Webster does list endless as a synonym for infinite. So we should be able to accept that infinite means endless.

0.999... represents an endless series of nines. 0.000...1 represents an endless series of zeroes with a one at the end. Let's explore that sentence: an endless series of zeroes with a one at the end. That is impossible. You cannot have an endless sequence that has an endpoint. You cannot have an infinite sequence that has an endpoint. So there is no 0.000...1 number that you can add to 0.999... to make 1. The series of zeroes would have to continue forever, and an endless series of zeroes is equal to zero. So 0.999... must equal 1.

 

[OCGuy]

Originally posted by: her209
I made this for you guys.
http://pics.bbzzdd.com/users/h...9/Philosoraptor999.jpg

Fixed

 

[oiprocs]

Imagine the chaos if this thread had more timewarps.

 

[hanoverphist]

i love reading this argument. by far, it is more entertaining than any others here.

 

[DisgruntledVirus]

Originally posted by: DrPizza

Originally posted by: rocadelpunk
It's sad that the majority's understanding of mathematics is akin to reading at a 4th grade level.

And, sadly, a lack of reading ability by someone has no effect on my life, or arguably, a positive effect on my life. Sure, they can't fill out a job application, but hey, occasionally I like to go to McDonalds during the day for lunch, at a time when the teenagers are all at school. Ding, fries are done, you don't need to read to do that job.


But, when people are poor at math, and can read, they can affect national policy and decision making. Oh no! Executives got 137 million dollars out of a 40 billion bailout! Off with their heads! Grumble grumble to the politicians.

"They got 137 million out of 40,000 million. Oh, that's not so bad, that's a drop in the bucket."

The government is going to spend 942 million dollars on <blank>
"Outrage!"
The government is going to spend 1.5 billion dollars on <blank>
"oh, that's not as much."


Now, "million" and "billion" are what grade concepts? I don't even think it's 4th grade, is it? Oh, wait, he said akin to reading at the 4th grade level. Not 4th grade level mathematics. Since most people need a calculator to add 2 three digit numbers together, or to multiple two 2-digit numbers, I think it's arguable that they lack some of the math skills of even a 3rd grader (not that they don't have a subset of skills of later grades.)

Thank god I'm one of the few who can.

Have beaten many friends who have had to rely on a calculator (on their phone/computer/etc) and arrived at the correct answer faster than they could with their calculator. Granted I do multiplication different than the average person (72*39 I'll round to 72*4=288 and add the 0 to the end so 2880, then subtract 72 for 2808. For numbers that aren't 0, 1, 9 as the last digit like 54*76 I'll do (50*76)+(4*76)=3800+304=4104), and by breaking it down into easier sub-problems I can arrive at the answer quite quickly.

It's a geek thing that can be used to make people go ":Q😕 how the hell?!?!?!" I also used to play a game when I worked at CVS where I would try to get the total price (with tax) before I hit the total key on the register and see how accurate I was. Got to be quite good at it actually.

 

[LordMorpheus]

Did your roommate pay up? I've skimmed but haven't seen any reference to it once the high school dropouts came in and turned this thread into a farce.

 

[OCGuy]

So did you give him 5 $20s or did you go with the Franklin?

 

[mjrpes3]

Originally posted by: silverpig
ANYONE can post something on the archive.

Did you even look at the article? Granted it wasn't the most well written but it put an interesting twist on the problem using non-standard analysis. I'm not a mathematician but the article seems at least worthy of a response.

 

[Schfifty Five]

Originally posted by: OCguy
So did you give him 5 $20s or did you go with the Franklin?

Neither, he received $99.999...

 

[91TTZ]

Originally posted by: GodlessAstronomer

Originally posted by: OCguy
It doesnt.

You are incredibly stupid.

In some disciplines such as philosophy they'd say it doesn't equal 1. If it was 1, they'd call it 1. But since it's .999..., it's smaller than 1 by the smallest possible fraction, an immeasurable amount.

In calculus it equals 1.

 

[halik]

Originally posted by: 91TTZ

Originally posted by: GodlessAstronomer

Originally posted by: OCguy
It doesnt.

You are incredibly stupid.

In some disciplines such as philosophy they'd say it doesn't equal 1. If it was 1, they'd call it 1. But since it's .999..., it's smaller than 1 by the smallest possible fraction, an immeasurable amount.

In calculus it equals 1.

It cannot be smaller by the smallest fraction, because that would imply the infinite series of 9 ends somewhere

 

[Dari]

So what is 1/3x3?

 

[Turin39789]

do parallel lines exist?

 

[Dari]

Originally posted by: Turin39789
do parallel lines exist?

A mathematician will say yes and an engineer will say no. They're both correct but it obviously depends on the conditions.

 

[OCGuy]

Is there a perfect circle?

Can a computer truely randomize a number or pattern?

 

[GodlessAstronomer]

Originally posted by: Turin39789
do parallel lines exist?

Depends on the type of geometry. Euclidean geometry includes parallel lines as a distinguishing axiom. Some people believe that Euclid's parallel postulates has never been proved. Non-Euclidean geometries don't necessarily have parallel lines (see elliptic geometry or hyperbolic geometry).