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.999.... (Repeating) is equal to one?

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Enthryn (they/them) Since: Nov, 2010
(they/them)
#101: Sep 9th 2011 at 10:56:14 PM

The real numbers are one of the most fundamental structures in mathematics. It's the primary object of study in many branches of math, and it's key to our understanding of the concept "number". Therefore, we want to understand it as fully as possible.

USAF713 I changed accounts. from the United States Since: Sep, 2010
I changed accounts.
#102: Sep 9th 2011 at 11:05:51 PM

So, is .999 = to 1, or not...?

I am now known as Flyboy.
Clarste One Winged Egret Since: Jun, 2009 Relationship Status: Non-Canon
One Winged Egret
#103: Sep 9th 2011 at 11:06:47 PM

Well, 0.999 isn't, but 0.999... is.

DarkConfidant Since: Aug, 2011
#104: Sep 9th 2011 at 11:07:51 PM

Yes, it is.

.999... = 9/10 + 9/100 + 9/1000 + ...

This is an infinite geometric series with first term 9/10 and common ratio 1/10.

The sum of the infinite series is a/(1-r), where a is the first term and r is the common ratio. The sum is therefore (9/10)/(1-(1/10)) = (9/10)/(9/10) = 1. QED.

USAF713 I changed accounts. from the United States Since: Sep, 2010
I changed accounts.
#105: Sep 9th 2011 at 11:09:29 PM

So, I was right in saying .999 = 3/3 = 1?

So... where is the debate?

I am now known as Flyboy.
DarkConfidant Since: Aug, 2011
#106: Sep 9th 2011 at 11:10:38 PM

Seems like it's just people being confused. But yeah, that's effectively correct.

USAF713 I changed accounts. from the United States Since: Sep, 2010
I changed accounts.
#107: Sep 9th 2011 at 11:12:45 PM

Mathematicians always try to make everything as complex as it possibly can be, it seems.

I'll just go back to my soft science corner, I guess. I'm never welcome in math discussions...

I am now known as Flyboy.
Enkufka Wandering Student ಠ_ಠ from Bay of White fish Since: Dec, 2009
Wandering Student ಠ_ಠ
#108: Sep 9th 2011 at 11:15:16 PM

and its those kinds of generalizations that make math seem hard to understand.

You want simple? slice an orange in half. (1/2+1/2)

Slice one half of the half in half.(1/2+1/4+1/4)

keep doing it to the halves.(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256...)

you will get slices so infinitely small, but you will still be slicing. add them all up, you get a whole orange.

edited 9th Sep '11 11:16:45 PM by Enkufka

Very big Daydream Believer. "That's not knowledge, that's a crapshoot!" -Al Murray "Welcome to QI" -Stephen Fry
USAF713 I changed accounts. from the United States Since: Sep, 2010
I changed accounts.
#109: Sep 9th 2011 at 11:16:45 PM

I don't think math is hard to understand because of the math (although at a certain level—somewhere around high school trigonometry—this becomes true), I think it's hard to understand because mathematicians tend to explain things under the assumption that everyone was good at math like them...

edited 9th Sep '11 11:17:13 PM by USAF713

I am now known as Flyboy.
BlackHumor Since: Jan, 2001
#110: Sep 9th 2011 at 11:18:26 PM

@USAF: Not quite, because the ... is essential.

.999 is just .999. .999... is what's equal to 1.

USAF713 I changed accounts. from the United States Since: Sep, 2010
I changed accounts.
#111: Sep 9th 2011 at 11:19:27 PM

Well, that would be because of the little bar thing I can't do on this keyboard...

There's the other thing about hard studies (math and "proper" science): the technicalities. They're everywhere...

I am now known as Flyboy.
Enkufka Wandering Student ಠ_ಠ from Bay of White fish Since: Dec, 2009
Wandering Student ಠ_ಠ
#112: Sep 9th 2011 at 11:21:26 PM

start at addition.

Go to subtraction, introduces negative numbers.

go to multiplication, which is addition of addition (5x5=5+5+5+5+5)

go to division, introduces fractions.

and so on until you get to calculus. Its doing stuff to numbers, and they have to assume some things about what people know, otherwise it takes twice or four times as long to explain something.

Very big Daydream Believer. "That's not knowledge, that's a crapshoot!" -Al Murray "Welcome to QI" -Stephen Fry
deathjavu This foreboding is fa... from The internet, obviously Since: Feb, 2010
This foreboding is fa...
#113: Sep 10th 2011 at 12:21:27 AM

2

Look, you can't make me speak in a logical, coherent, intelligent bananna.
ekuseruekuseru 名無しさん from Australia Since: Oct, 2009
名無しさん
#114: Sep 10th 2011 at 12:33:36 AM

Dear USAF,

You said:

"Mathematicians always try to make everything as complex as it possibly can be, it seems."

Here's why:

"the technicalities. They're everywhere..."

"mathematicians tend to explain things under the assumption that everyone was good at math like them"

Simplified explanations to complex problems are prone to having technical problems are relying on assumptions based on mathematical knowledge. Hence, complex explanations, when the problem is complex, are a better option.

edited 10th Sep '11 12:35:45 AM by ekuseruekuseru

TheStupidExclamationMark Orbs from In ur cupboard Since: Dec, 2009
Orbs
#115: Sep 10th 2011 at 1:08:11 AM

Can we just agree that 0.999... = 1 is one of those things that works theoretically, but once you try to represent it in the real world it fails miserably because the real world unfortunately doesn't deal with infinity?

I'd say that the difference between 0.999... and 1 is 1/infinity, which approaches zero (infinitely), just like 0.999... approaches 1 (infinitely), so you can effectively say 1/infinity = 0 and 0.999.... = 1, even if there theoretically is an infinitely small difference...

Now since the real world doesn't deal with infinity (it rounds at a certain point), having a computer calculate 1/3 x 3 will not yield 1, but something slightly smaller...and that can lead to problems...

"That said, as I've mentioned before, apart from the helmet, he's not exactly bad looking, if a bit...blood-drenched." - juancarlos
TheDeadMansLife Lover of masks. Since: Nov, 2009
Lover of masks.
#116: Sep 10th 2011 at 1:24:14 AM

I thought the problem has to do with when you start dividing one by three and accidentally create an impossible number?Trollface.jpeg

edited 10th Sep '11 1:27:33 AM by TheDeadMansLife

Please.
Swish Long Live the King Since: Jan, 2001
Long Live the King
#117: Sep 10th 2011 at 1:38:20 AM

Question: If 0.999... is considered to = 1, is 0.000...001 considered = 0?

I've been curious about that...

Clarste One Winged Egret Since: Jun, 2009 Relationship Status: Non-Canon
One Winged Egret
#118: Sep 10th 2011 at 1:52:12 AM

Well, it only counts if there are an infinite number of zeroes before the final 1. And, because of the nature of infinity, that means there is no final 1, so it's just an infinite number of zeroes. Rather, that simply demonstrates another reason that 0.999... has to be equal to 1.

edited 10th Sep '11 1:52:34 AM by Clarste

KylerThatch literary masochist Since: Jan, 2001
literary masochist
#119: Sep 10th 2011 at 1:58:03 AM

I have a tangentially related question. Why is the matter of 0.999... = 1 so darn controversial?

This "faculty lot" you speak of sounds like a place of great power...
Clarste One Winged Egret Since: Jun, 2009 Relationship Status: Non-Canon
One Winged Egret
#120: Sep 10th 2011 at 2:07:19 AM

I have no idea. I'd imagine it's because "common sense" diverges from mathematical logic? Although I have no idea where people get their common sense ideas regarding an infinite series from.

Swish Long Live the King Since: Jan, 2001
Long Live the King
#121: Sep 10th 2011 at 2:22:47 AM

My only problem with the whole idea of infinity is that other than mathematical theory, there really isn't anything that is infinite(unless one believes in a Deity), is there?

And that's why I have a problem with an infinite number of nines. Because, at some point, it really does have to stop... And at that point, it's really doesn't equal one...

ekuseruekuseru 名無しさん from Australia Since: Oct, 2009
名無しさん
#122: Sep 10th 2011 at 2:44:03 AM

[up]

If it does stop, it's not infinite. And since we're speaking in the context of mathematical theory, your complaints (valid or not) are still not any reason to abandon the concept of infinity within mathematical theory (or other relevant fields).

The problem with infinity is not that it doesn't exist in the real world, so to speak, but rather, human experience and limits in perception mean that even with a working understanding, we might not truly grasp the idea.

This problem with infinity also seems to be the root of most peoples' problems with the thread topic.

CaissasDeathAngel House Lewis: Sanity is Relative from Dumfries, SW Scotland Since: Oct, 2010 Relationship Status: Pining for the fjords
House Lewis: Sanity is Relative
#123: Sep 10th 2011 at 6:49:37 AM

I'm not a mathematical person in the slightest, but I do understand this. The problem is that it seems irrational and illogical that a decimal could represent two numbers, or that there could be some difference between 0.99999999999 and 0.99999999999_

And yet, the fact that decimals are a poor representation of fractions due to numerical limits is easy to understand; it's why rounding (which is innately inaccurate) is used so often. What people can't do is make the connection between the flaws in decimalisation and their use as representatives of fractions.

My name is Addy. Please call me that instead of my username.
SavageHeathen Pro-Freedom Fanatic from Somewhere Since: Feb, 2011
Pro-Freedom Fanatic
#124: Sep 10th 2011 at 6:52:52 AM

0,333...=1/3.

0,999...=0,333...*3=3/3=1

It's actually that simple. Accepting that 0.999... equals 1 is much less absurd than accepting that 3/3 do not equal 1.

edited 10th Sep '11 6:55:04 AM by SavageHeathen

You exist because we allow it and you will end because we demand it.
DarkConfidant Since: Aug, 2011
#125: Sep 10th 2011 at 6:53:06 AM

If you think that the two numbers are not equal to one another, then logically, there's another number that should be less than .999... and 1. However, it is impossible to construct such a number, so the only conclusion is that the two are equal.


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