The "common sense" proof

[Raeven0]

im sure there are NUMEROUS mathimatical proofs the point to nine recurring doesnt equal one, right?

Premise: There cannot exist two contradictory valid proofs.
Reasoning: There exist valid proofs that point nine recurring equals one.
Conclusion: There cannot exist valid proofs that point nine recurring does not equal one.
Corollary: Point nine recurring equals one.

 

[Raxxman]

just as:

0.9.... = 1 = 3/3 = 9999999/9999999 = any number/the same number

saying otherwise only proves you don't understand. I don't want to sound mean but but that's the only way to say it.

 

[Sulkdodds]

im sure there are NUMEROUS mathimatical proofs the point to nine recurring doesnt equal one, right?

im not coming back to this thread, its pissing me off now :|

If you're so sure...you could try finding and posting them. Besides, you can't really have contradictory proofs.

 

[dfc05]

It's like how a number to the power of 0 is 1, instead of 0.

Don't question the principal, it just IS.

Actually there's a rather common sense way to see how it would be 1. This isn't a good proof or anything because I can't remember it, but anyways, say we're looking at powers of 2.

2^1 = 2
2^2 = 4
2^3 = 8
etc

So for each incremental power, you multiply by 2 right? Yay. Now go backwards, and you're dividing by two.

2^2 = 4
2^1 = 2
2^0 = 1 ??? WTH
2^-1 = 1/2
2^-2 = 1/4

Also, .9999... does equal 1.

Also, e^(pi*i) = -1. And again. So I couldn't bother to actually read through the whole thing because once anyone mentions Taylor series I'm like "Ugh, go away," but we also did it in Diff EQ. I can't quite remember how. My professor was really boring.

 

[jondy]

x^0=1 because x^i/x^i = 1

therefore x^(i-i)=1, so x^0 = 1

 

[Ennui]

it's equal to one and not equal to one, these sorts of mathematics were not meant to deal with infinity, arguing over it is just saying whether you use common sense or the rules

 

[dfc05]

x^0=1 because x^i/x^i = 1

therefore x^(i-i)=1, so x^0 = 1

Yeah, that way is a lot better .

 

[Raeven0]

arguing over it is just saying whether you use common sense or the rules

Mathematics is 0% common sense and 100% rules, even if you don't like it that way. Point nine recurring equals one.

 

[The Monkey]

This is the fourth thread on this subject. :|


0,999...=1

Perdiod

.

 

[Noobulon]

Wow, I've never read such an explosive thread about the number 1!
I guess I must have missed the other three versions of this thread.

Anyway, It may please somebody to know that as a maths peon, I've been successfully converted by this discussion.
Entering the thread, I was convinced that 1 and 0.999 recurring must be different numbers, with an infinitely small difference between them. My thought process went something like this:

.9999... infinite 9's. IT NEVER REACHES ONE. IT JUST GOES ON WITH NINES FOREVER AND EVER!!

Then somebody points out that the only "infinitely small" value is zero. Therefore the infinitely small difference between 1 and 0.999... is a difference of zero. So 0.999... = 1. :| Ah I see.

By the by, I think the argument in this thread has actually been about our definitions of "infinity"- and what it really means when we say there's an "infinite" series of digits, as with 0.999 recurring.

1/3 = 3/9 = 0.33333...

therfore 5/9 = 0.5555...

And 9/9 = 0.99999..... = 1.

x = 0.999...

multiply both sides by 10

10x = 9.999...

10x - x = 9.999... -0.999... (subtracting the same thing from both sides)


9x = 9

so

x = 1.

Point nine recurring is a single number. It DOES NOT "approach" anything because it is ONE NUMBER with ONE VALUE. If you attempted to transcribe point nine recurring on paper, THEN the number on your paper would approach point nine recurring AND one with each additional nine; but we are talking about THE NUMBER ITSELF, NOT the number as you try to write it out.

For your further edification, a series can have only one limit; point nine recurring, as it is written out, approaches both point nine recurring and one; therefore, point nine recurring must equal one, since they are both limits to the series.

^^ These arguments seem fully convincing to me as well. Thanks guys, I'm now 0.001823 less crap at maths!

 

[Beerdude26]

...

Y'all do know that there are NUMEROUS mathematical proofs that point nine recurring equals one, right?

If you can't show how ALL of them are wrong, I suggest you stfu.

Point nine recurring is a single number. It DOES NOT "approach" anything because it is ONE NUMBER with ONE VALUE. If you attempted to transcribe point nine recurring on paper, THEN the number on your paper would approach point nine recurring AND one with each additional nine; but we are talking about THE NUMBER ITSELF, NOT the number as you try to write it out.

For your further edification, a series can have only one limit; point nine recurring, as it is written out, approaches both point nine recurring and one; therefore, point nine recurring must equal one, since they are both limits to the series.

This is the correct answer.

0.99... (Yes this is how it is supposed to be written lol) as an approach to 1 would indeed equal 1.
0.99 --> to infinity (Not how it is supposed to be written, I'm trying not to confuse you guys) as a DEFINITE number would never equal 1. An example of this would be the system (Or whatever you guys call it lol):

{x=0.99 --> to infinity
{x=1

This system would be invalid, because x has different values.

 

[TheSomeone]

I've noticed that every thread created on the subject, more and more people agree that .999... = 1.

The first one I created i didn't have a single soul on my side until like 8 pages in when ikerous came.

 

[Narcolepsy]

Premise: There cannot exist two contradictory valid proofs.
Reasoning: There exist valid proofs that point nine recurring equals one.
Conclusion: There cannot exist valid proofs that point nine recurring does not equal one.
Corollary: Point nine recurring equals one.

I've learned from dabbling in psychology that some people simply don't trust or grasp the principles of cold, hard logic. Unfortunately, mathematics is in fact governed by cold, hard logic, despite any desperate attempts by the more emotional ones among us at "common sense", meaning that there are some people on this earth that we will NEVER be able to convince that .999... = 1, casting all of the math nerds of the world into some sort of freakish mathematical hell FROM WHICH THERE IS NO ESCAPE.

I've noticed that every thread created on the subject, more and more people agree that .999... = 1.

The first one I created i didn't have a single soul on my side until like 8 pages in when ikerous came.

Excellent! If you express this empirical observation as a fraction in which the denominator = the population of halflife2.net = C and the numerator = the converted population of halflife2.net = n, then lim (n -> C) n/C = .999... = 1.

ARGUMENT OVER.

 

[Beerdude26]

I've noticed that every thread created on the subject, more and more people agree that .999... = 1.

Good.

You were never actually wrong. And it's written .99...

 

[Beerdude26]

I've learned from dabbling in psychology that some people simply don't trust or grasp the principles of cold, hard logic. Unfortunately, mathematics is in fact governed by cold, hard logic, despite any desperate attempts at "common sense", meaning that there are some people on this earth that we will NEVER be able to convince that .999... = 1, casting all of the math nerds of the world into some sort of freakish mathematical hell FROM WHICH THERE IS NO ESCAPE.

/me points at Ikerous

EDIT: Aww crap, I double posted.

D:

 

[TheSomeone]

Ikky wont be posting any time soon

 

[Beerdude26]

Ikky wont be posting any time soon

How come?

 

[TheSomeone]

Girlfriend

 

[Beerdude26]

Girlfriend

She'll decay over time.

Nah jk, I'll let him have fun

 

[TheSomeone]

Decay or moo.

(shes actually very cool)

 

[Beerdude26]

Decay or moo.

(shes actually very cool)

Judging from the awesomeness that is Ikerous, I'm sure she is.

Anyways, back on topic.
Wait, we already solved it :|

kk then.

Tea?

 

[Raeven0]

I've learned from dabbling in psychology that some people simply don't trust or grasp the principles of cold, hard logic. Unfortunately, mathematics is in fact governed by cold, hard logic, despite any desperate attempts by the more emotional ones among us at "common sense", meaning that there are some people on this earth that we will NEVER be able to convince that .999... = 1, casting all of the math nerds of the world into some sort of freakish mathematical hell FROM WHICH THERE IS NO ESCAPE.

This post wins.

 

[DreadLord]

why Won't This Topic Just Die. Even The Penis Length Discussion Ended Because Everyone Wanted 5.999...? Inch Pen0rs!!

Oh My God!!

<2.999..?

 

[jondy]

Even The Penis Length Discussion Ended Because Everyone Wanted 5.999...? Inch Pen0rs!!

MY PENIS TENDS TOWARD INFINITY

 

[_Z_Ryuken]

What logical application is there for .99...?
If it is equal to 1, the more complex representation must be pointless, correct?

 

[Krynn72]

Ok, so this is my first .9999 = 1 thread, so im not up to date on all the theories and whatnot. Indeed, I only read the first page of this thread because I know the answer.

.9 repeating does not equal 1 because it is always an infinately small number away from being 1. There is no way in all hell that it equals 1. The only thing to equal 1 is 1 because they lie on the same exact point on a number line. No matter how accurate you get, 1 is 1. But, if you run out .9 repeating, it will never become 1, because its always some tiny tiny miniscule bit less than one. Like I said, its always an infinately smaller number away from being equal to one.

To think anything else is ridiculous. Does .8 repeating equal .9? No. The same applies for any number that repeats infinately.

Now, if your implying that the difference between .9 repeating and 1 is negligible, then I would agree. Its so close it doesnt matter.

But even an 8th grade math student knows that .9 repeating is not 1.

 

[Terminator]

.9999' does not physically equal 1.
But for the sake of simple maths and computers, it does.

I have said what is correct.

 

[_Z_Ryuken]

Ok, so this is my first .9999 = 1 thread, so im not up to date on all the theories and whatnot. Indeed, I only read the first page of this thread because I know the answer.

.9 repeating does not equal 1 because it is always an infinately small number away from being 1. There is no way in all hell that it equals 1. The only thing to equal 1 is 1 because they lie on the same exact point on a number line. No matter how accurate you get, 1 is 1. But, if you run out .9 repeating, it will never become 1, because its always some tiny tiny miniscule bit less than one. Like I said, its always an infinately smaller number away from being equal to one.

To think anything else is ridiculous. Does .8 repeating equal .9? No. The same applies for any number that repeats infinately.

Now, if your implying that the difference between .9 repeating and 1 is negligible, then I would agree. Its so close it doesnt matter.

But even an 8th grade math student knows that .9 repeating is not 1.

After someone posted something that actually made sense, it sunk in. What the concept is, is not any finite number like .9999999999999999999999, it's saying if you have a number with an infinite number of 9s after the decimal it is equal to the next highest number, be it 1, 2, 3, or whatever. It really is pointless to even think about it, as a number with infinite values after the decimal is not practical or even useful.
0.9 with 9s repeating forever is equal to 1. That is a fact. The only reason it is a fact is because it is considered a complex representation of 1. 4.99... repeating forever is a complex representation of 5. The numbers with infinite repeating values are useless in that state so they can exist only as complex representations for mathematicians to giggle about. This is my conclusion.

I also would like to know what .88... repeating is "equal" to.

 

[Narcolepsy]

I also would like to know what .88... repeating is "equal" to.

My guess is that it's a "dark number", beyond the comprehension of the human mind. These "dark numbers" form the mathematical basis of dark matter, which makes up over 90% of our universe.

It's pretty easy, really. Don't understand something? Just slap the word "dark" on it and throw it in a scientific journal, and you've got yourself a new theory.

 

[TheSomeone]

Ok, so this is my first .9999 = 1 thread, so im not up to date on all the theories and whatnot. Indeed, I only read the first page of this thread because I know the answer.

.9 repeating does not equal 1 because it is always an infinately small number away from being 1. There is no way in all hell that it equals 1. The only thing to equal 1 is 1 because they lie on the same exact point on a number line. No matter how accurate you get, 1 is 1. But, if you run out .9 repeating, it will never become 1, because its always some tiny tiny miniscule bit less than one. Like I said, its always an infinately smaller number away from being equal to one.

To think anything else is ridiculous. Does .8 repeating equal .9? No. The same applies for any number that repeats infinately.

Now, if your implying that the difference between .9 repeating and 1 is negligible, then I would agree. Its so close it doesnt matter.

But even an 8th grade math student knows that .9 repeating is not 1.

.9999' does not physically equal 1.
But for the sake of simple maths and computers, it does.

I have said what is correct.

No.

FFS
DID YOU ALL FAIL REMEDIAL ALGEBRA?

What math is unpure about this????

x = 0.999...

multiply both sides by 10

10x = 9.999...

10x - x = 9.999... -0.999... (subtracting the same thing from both sides)


9x = 9

so

x = 1.

__________________________________________________________

I also would like to know what .88... repeating is "equal" to.

.1111... = 1/9
.222.... = 2/9
etc...
.8888.... = 8/9
.999.... = 9/9

 

[Raeven0]

Point eight recurring equals 8/9, or 8(1/9), or (8)(9^-1).

You two extras who think point nine recurring is not exactly equivalent to one need to look over THE PROOFS THAT HAVE BEEN POSTED HERE A THOUSAND TIMES.

No, you mathematical plebe, an eight-grade student could EASILY tell you that 0.89 lies between point eight recurring and point nine recurring, therefore POINT EIGHT RECURRING DOES NOT EQUAL POINT NINE RECURRING. An eighth-grade student could also tell you that there exists NO real number between point nine recurring and one, meaning THEY ARE THE SAME NUMBER.

 

[TheSomeone]

People for 0.99... = 1:
MATHEMATICALPROOFLOGICALPROOFMATHMATHMATH
People against 0.99... = 1:
lol dey are obviouzly da different numberz dey dun look the saym

 

[Raeven0]

People for 0.99... = 1:
MATHEMATICALPROOFLOGICALPROOFMATHMATHMATH
People against 0.99... = 1:
lol dey are obviouzly da different numberz dey dun look the saym

Pretty much.
;(

 

[Dumb Dude]

People for 0.99... = 1:
MATHEMATICALPROOFLOGICALPROOFMATHMATHMATH
People against 0.99... = 1:
lol dey are obviouzly da different numberz dey dun look the saym

So then why continue the with the threads? If people don't get it, they don't get it. No need to keep on and on and on and on and on about it.

 

[Raeven0]

I retract this post. My inferior mind placed an imaginary extra verb in the quote that completely changed its meaning...

 

[TheSomeone]

So then why continue the with the threads?

Comic releif?

It should be obvious by now I just make these threads because they're fun.
EDIT: hahahha, on this poinst Raeven0, i must disagree

 

[Shippi]

stfu with these threads already D: