Is 1 = 0.9999......

[MadRat]

The ad hominum continues. Par for your course, Ross.

 

[DrPizza]

It's been several days since I offered a $100 bet. *sigh* Looks like I won't any "easy" Christmas money. (although, the conditions set would have resulted in a lot of work contacting math departments of universities. Maybe I should have made it $1000?)

Non-math people arguing that .999... != 1 make as much sense as a non-Spanish speaking person arguing that "el gato" != "the cat" ---It's close to a cat, but not quite a cat. It means almost the same thing...


p.s. Since I'm one of those non-spanish speaking people I referred to, I do hope my spanish vocabulary was okay... afaik, el gato could actually mean toilet.

 

[Chu]

Originally posted by: DrPizza
It's been several days since I offered a $100 bet. *sigh* Looks like I won't any "easy" Christmas money. (although, the conditions set would have resulted in a lot of work contacting math departments of universities. Maybe I should have made it $1000?)

Non-math people arguing that .999... != 1 make as much sense as a non-Spanish speaking person arguing that "el gato" != "the cat" ---It's close to a cat, but not quite a cat. It means almost the same thing...


p.s. Since I'm one of those non-spanish speaking people I referred to, I do hope my spanish vocabulary was okay... afaik, el gato could actually mean toilet.

Considering i'm on the eq. of a 2400bps modem right now, out of curiosity, what was the bet?

-Chu

 

[Kyteland]

The $100 bet!!

Originally posted by: DrPizza
No way, YamahaXS, I've read the entire thread (not all at once, but catch up every time I see it)...

Let me pose this question for bleeb and any others who think they're correct that .999... != 1
would you be willing to wager $100 on it? (I'm willing to bet that .999repeating EQUALS EXACTLY 1)

To settle the bet, 1st we each put our $100 someplace where the loser can't renig. Then, we put the names of all accredited universities that have a math program in a hat (or narrow the choices to just U.S. universities to eliminate the language barrier... I'm not sure I'd know how to ask profs at a chinese university). We then pull out 10 names at random and contact the math faculty of those universities. We'll go with whatever the majority of them agree upon (actually, I'd almost be willing to bet an additional $100 that it'll be unanimous that they say .999repeating = exactly 1.

Then again, that would be followed with someone starting a thread about how 10 out of 10 randomly selected college level math programs...



Let me offer not a proof, but perhaps a visual demonstration that some of you may be able to follow (can't remember if this one was shown yet or not)

2/7 = .285714285714285714285714285714285714285714285714285714...
5.7 = .714285714285714285714285714285714285714285714285714285...

Note: 2/7 + 5/7 equals exactly 1
Now, notice what happens if you were to add the two.
you get .99999999999999999999999999999999 repeating forever.

 

[FoBoT]

this thread has almost 1700 posts and i have never read/posted in it

what is it aboot ?

 

[Kyteland]

Originally posted by: Kyteland
The $100 bet!!

Originally posted by: DrPizza
No way, YamahaXS, I've read the entire thread (not all at once, but catch up every time I see it)...

Let me pose this question for bleeb and any others who think they're correct that .999... != 1
would you be willing to wager $100 on it? (I'm willing to bet that .999repeating EQUALS EXACTLY 1)

To settle the bet, 1st we each put our $100 someplace where the loser can't renig. Then, we put the names of all accredited universities that have a math program in a hat (or narrow the choices to just U.S. universities to eliminate the language barrier... I'm not sure I'd know how to ask profs at a chinese university). We then pull out 10 names at random and contact the math faculty of those universities. We'll go with whatever the majority of them agree upon (actually, I'd almost be willing to bet an additional $100 that it'll be unanimous that they say .999repeating = exactly 1.

Then again, that would be followed with someone starting a thread about how 10 out of 10 randomly selected college level math programs...



Let me offer not a proof, but perhaps a visual demonstration that some of you may be able to follow (can't remember if this one was shown yet or not)

2/7 = .285714285714285714285714285714285714285714285714285714...
5.7 = .714285714285714285714285714285714285714285714285714285...

Note: 2/7 + 5/7 equals exactly 1
Now, notice what happens if you were to add the two.
you get .99999999999999999999999999999999 repeating forever.

Edit: DrPizza, I see a flaw in your bet. If I were to take you up on both, I could then offer each of the depts $40 to agree that 1 != 0.9999 repeating. If one of them takes the offer, then the two $100 bets cancel out and I'm out $40, but if 5 take me up on it then I win both bets and make enough $$ from you to pay them off. :evil:

Real Edit: WTF?!? I swear I hit edit on the other post, not quote.

*shrug * postcount++

 

[HomeBrewerDude]

did you know there is an infinity symbol?

??


ALT+236

then again maybe not

ahh there it is. ∞

╝∞
ALT+236 is it afterall
∞∞∞∞∞∞

 

[Yax]

Originally posted by: Kyteland
The $100 bet!!

Originally posted by: DrPizza
No way, YamahaXS, I've read the entire thread (not all at once, but catch up every time I see it)...

Let me pose this question for bleeb and any others who think they're correct that .999... != 1
would you be willing to wager $100 on it? (I'm willing to bet that .999repeating EQUALS EXACTLY 1)

To settle the bet, 1st we each put our $100 someplace where the loser can't renig. Then, we put the names of all accredited universities that have a math program in a hat (or narrow the choices to just U.S. universities to eliminate the language barrier... I'm not sure I'd know how to ask profs at a chinese university). We then pull out 10 names at random and contact the math faculty of those universities. We'll go with whatever the majority of them agree upon (actually, I'd almost be willing to bet an additional $100 that it'll be unanimous that they say .999repeating = exactly 1.

Then again, that would be followed with someone starting a thread about how 10 out of 10 randomly selected college level math programs...



Let me offer not a proof, but perhaps a visual demonstration that some of you may be able to follow (can't remember if this one was shown yet or not)

2/7 = .285714285714285714285714285714285714285714285714285714...
5.7 = .714285714285714285714285714285714285714285714285714285...

Note: 2/7 + 5/7 equals exactly 1
Now, notice what happens if you were to add the two.
you get .99999999999999999999999999999999 repeating forever.

Lets bet $99.99... over it instead.

Can't believe this thread keeps coming back to life. People, just forget trying to convince the losers of the truth. Its like trying to tell children that Santa doesn't exist. They'd never believe you.

Even if we got all the Profs of the major universities to make statements that the numbers are equal, these pea brains will just say the Profs are wrong.:|

So please just move on and let the thread die.

 

[HomeBrewerDude]

Originally posted by: cheapbidder01 Lets bet $99.99... over it instead. Can't believe this thread keeps coming back to life. People, just forget trying to convince the losers of the truth. Its like trying to tell children that Santa doesn't exist. They'd never believe you. Even if we got all the Profs of the major universities to make statements that the numbers are equal, these pea brains will just say the Profs are wrong.:| So please just move on and let the thread die.

no way. not after me hitting ALT+xyz until I found the ??


edit ah fvckit i am going home.

 

[Hector13]

Originally posted by: MadRat
The ad hominum continues. Par for your course, Ross.

your side of the argument would be soooo easy to prove were it right. You claim .99... is less than one, so 1 - .9999... = x (where x > 0).

Just tell me what number x is, and I'll believe you. Then you can tell me what x/2 is or x/10 or what .9999... + x/2 is!

 

[MadRat]

Likewise, tell us all what number comes right before .999... and then we can cut the line up into equal segments and measure that sliver between .999... and 1. Either there can be a number before .999... or the value didn't exist in the first place. I'm sure we could probably use base infinity to prove your point somehow...

Your group refuses to define what you mean that is does exist when .999... has no definitive fraction that can represent it. You math geniuses refuse to give up the notion that .999... does exist on the number line in the same way as real numbers. The value of .999... is not something which we can represent with nice round numbers, like .5 and 2, which makes it impossible to pinpoint an exact placement of the value between any two other numbers. Yet at least one of you insists its there between something like 0 and 2. Sorry, but while I agree its approximately between the 0 and 2, its not exactly positioned on a segment anywhere. Then again someone said Pi had an exact value on that same real number line, too, which is not true because it can only be approximated and never defined by a definitive number.

 

[MAME]

madrat, there is no number right before any number. You failed math 101 or something?

 

[godspeedx]

Originally posted by: DrPizza

Originally posted by: godspeedx
I know that .9 repeating is equal to 1, but I just thought of a different proof. Possibly.

1/3 = .3 repeating
2/3 = .6 repeating
3/3 = .9 repeating
3/3 = 1

Is that a proof?

Not a proof, but *SHOULD* be a reasonable enough illustration of the fact that would convince most people. But then again, there are still people who believe the earth is flat, no matter what they're told... no matter what evidence is presented to them. Unfortunately, it's now appearing that a subset of those people are posting in this thread on ATOT.

What an interesting observation!

 

[MadRat]

By the way, if .999... represents a tail of 9's that proceeds to infinity and 1.0 has a tail of 0's that proceed to infinity then its no different that tryng to compare .9 to 1.0, because there is going to be a sliver left. Even when you proceed to infinity the sliver will be there, even if there is not a fixed location. If we take .999... and times it by 10^(infinity) then we end up with an infinity number of nines that extend beyond zero, correct? Basically we shifted the decimal to the right of the nines. Substitute y for (.999... times 10^(infinity)) to simplify the demonstration. If we take 1.0 and times it be 10^(infinity) then we end up with a value that is 1 greater than y, otherwise equal to (.999... times 10^(infinity))+1. Substitute x for (1.0... times 10^(infinity)) to simplify the math and we get a difference of exactly 1. Philosophically it works this way, but whether you math experts want to accept it or not is up to you.

x = 1.0... times 10^(infinity) = (.999... times 10^(infinity))+1
y = (.999... times 10^(infinity))

x - y = 1

 

[godspeedx]

Originally posted by: MAME
madrat, there is no number right before any number. You failed math 101 or something?

Lol, yeah and I think he supported the argument he's trying to disprove somewhere in that mess.

 

[MadRat]

Originally posted by: MAME
madrat, there is no number right before any number. You failed math 101 or something?

When you break a line into equal segments then we can determine a value of measure. The numbers 1, 2 and 3 fall on positions that can be measured using exactly equidistant line segments. The value of .999... would not fall on any segment of measure, therefore no exact position can be established for it. You want to argue semantics, but you ignore the meaning of the explanation.

 

[dighn]

Originally posted by: MadRat
x = 1.0... times 10^(infinity) = (.999... times 10^(infinity))+1
y = (.999... times 10^(infinity))

x - y = 1

how can you add 1 to the end of something that has no end? it makes no sense.

 

[MadRat]

Perhaps you should ask the guys that claim definitive value can be assigned for something that may not exist in the first place...

 

[MAME]

MadRat, please listen to me. Stop posting in this thread. Go to a college. Talk to the Math department. Then you can come back and tell us how you got owned so bad, you walked crooked for a week.

Otherwise you're just spewing crap out of your mouth that's a waste of time to correct.

I'm being serious, TALK TO SOMEONE WHO KNOWS ABOUT THIS STUFF. Go to a college, I beg of you.

 

[DrPizza]

Originally posted by: MadRat

Originally posted by: MAME
madrat, there is no number right before any number. You failed math 101 or something?

When you break a line into equal segments then we can determine a value of measure. The numbers 1, 2 and 3 fall on positions that can be measured using exactly equidistant line segments. The value of .999... would not fall on any segment of measure, therefore no exact position can be established for it. You want to argue semantics, but you ignore the meaning of the explanation.

For what it's worth... let's do a little geometry.(I anticipate madrat will find a problem with this somewhere...)
Construct 2 parallel number lines, located exactly 1 unit apart from each other.

Starting at 0 on the first number line, draw a line through the 1 on the second number line. Make this new line with 0 being in the same place as zero on the first number line. The *EXACT* location of the square root of 2 is where the diagonal number line intersects the 2nd number line.

Hey, but wait a second... doesn't the square root of 2 have an infinite number of decimal places?
(But, I suppose madrat doesn't believe in geometry too??)
--------------------------------------------------------------------------------------------------------------------

And, here's one to blow your mind, madrat.
Make a triangle.
Draw a segment through the triangle parallel to the base side of the triangle, ending at each edge of the triangle.
..../\
.../..\
../---\
./......\
-------- (ignore the dots... hopefully you get the idea.

Now, there are just as many points on the line segment going through the center of the triangle as there are on the base of the triangle, even though the base of the triangle is longer. To prove this, here's a 1 to 1 correspondence: Use the left side of the triangle to show the left endpoints correspond to each other. Use the right side of the triangle to show the right endpoints correspond to each other also. Now, for *ANY* point on either the short segment or the bottom, draw a line extending to the vertex at the top of the triangle (and to the base of the triangle). The point where this line intersects the short segment corresponds to where the line intersects the base. Now, here's the challenge: Find a point that doesn't have a corresponding point. You can't. Therefore, there must be the same number of points on each.

(heh heh)

 

[MAME]

Originally posted by: DrPizza

Originally posted by: MadRat

Originally posted by: MAME
madrat, there is no number right before any number. You failed math 101 or something?

When you break a line into equal segments then we can determine a value of measure. The numbers 1, 2 and 3 fall on positions that can be measured using exactly equidistant line segments. The value of .999... would not fall on any segment of measure, therefore no exact position can be established for it. You want to argue semantics, but you ignore the meaning of the explanation.

For what it's worth... let's do a little geometry.(I anticipate madrat will find a problem with this somewhere...)
Construct 2 parallel number lines, located exactly 1 unit apart from each other.

Starting at 0 on the first number line, draw a line through the 1 on the second number line. Make this new line with 0 being in the same place as zero on the first number line. The *EXACT* location of the square root of 2 is where the diagonal number line intersects the 2nd number line.

Hey, but wait a second... doesn't the square root of 2 have an infinite number of decimal places?
(But, I suppose madrat doesn't believe in geometry too??)
--------------------------------------------------------------------------------------------------------------------

And, here's one to blow your mind, madrat.
Make a triangle.
Draw a segment through the triangle parallel to the base side of the triangle, ending at each edge of the triangle.
..../\
.../..\
../---\
./......\
-------- (ignore the dots... hopefully you get the idea.

Now, there are just as many points on the line segment going through the center of the triangle as there are on the base of the triangle, even though the base of the triangle is longer. To prove this, here's a 1 to 1 correspondence: Use the left side of the triangle to show the left endpoints correspond to each other. Use the right side of the triangle to show the right endpoints correspond to each other also. Now, for *ANY* point on either the short segment or the bottom, draw a line extending to the vertex at the top of the triangle (and to the base of the triangle). The point where this line intersects the short segment corresponds to where the line intersects the base. Now, here's the challenge: Find a point that doesn't have a corresponding point. You can't. Therefore, there must be the same number of points on each.

(heh heh)

Logic and examples aren't enough to change his mind

 

[Chu]

Madrat, before you make another post, PLEASE define "definitie value," "segment," "real number," and "...". It is very obvious that you are not using the standard definitions of these, and because of that your arguments as stated are making very little sense . . .

-Chu

 

[Chu]

Originally posted by: MadRat

Originally posted by: MAME
madrat, there is no number right before any number. You failed math 101 or something?

When you break a line into equal segments then we can determine a value of measure. The numbers 1, 2 and 3 fall on positions that can be measured using exactly equidistant line segments. The value of .999... would not fall on any segment of measure, therefore no exact position can be established for it. You want to argue semantics, but you ignore the meaning of the explanation.

If I'm reading this correctly, your essentially trying to state that if a number is not rational, it cannot be on the number line. Rational defined as the ratio of two intergers, such as 9/230, 2/139, 1/20000000000034, etc.

The problem is, the number line defined as such has holes. One of the most famous proofs in mathematics, that even a 4th grader can understand (and yes, it has been presented to 4th graders before), is that your line is missing numbers:

Therom : There does not exist a rational number x s.t. x*x=2 (i.e. the square root of 2)

Proof* :

1. Assume that √2 is a rational number. Meaning that there exists an integer a and b so that a / b = √2.
2. Then √2 can be written as an irreducible fraction (the fraction is shortened as much as possible) a / b such that a and b are coprime integers and (a / b)² = 2.
3. It follows that a² / b² = 2 and a² = 2*b².
4. Therefore a² is even because it is equal to 2*b² which is obviously even.
5. It follows that a must be even. (Odd numbers have odd squares and even numbers have even squares.)
6. Because a is even, there exists a k that fullfills: a = 2*k.
7. We insert the last equation of (3) in (6): 2b² = (2k)² is equivalent to 2b² = 4k² is equivalent to b² = 2k².
8. Because 2k² is even it follows that b² is also even which means that b is even because only even numbers have even squares.
9. By (5) and (8) a and b are both even, which contradicts that a / b is irreducible as stated in (2).

----------------------

Are you fine that your number line has holes in it? If yes, then, well, it's no surprise your having so much trouble that .999... = 1.

-Chu

*Proof formatting taken from the Wikipedia

 

[RossGr]

Originally posted by: MadRat
Likewise, tell us all what number comes right before .999... and then we can cut the line up into equal segments and measure that sliver between .999... and 1. Either there can be a number before .999... or the value didn't exist in the first place. I'm sure we could probably use base infinity to prove your point somehow...

Your group refuses to define what you mean that is does exist when .999... has no definitive fraction that can represent it. You math geniuses refuse to give up the notion that .999... does exist on the number line in the same way as real numbers. The value of .999... is not something which we can represent with nice round numbers, like .5 and 2, which makes it impossible to pinpoint an exact placement of the value between any two other numbers. Yet at least one of you insists its there between something like 0 and 2. Sorry, but while I agree its approximately between the 0 and 2, its not exactly positioned on a segment anywhere. Then again someone said Pi had an exact value on that same real number line, too, which is not true because it can only be approximated and never defined by a definitive number.

It is not a matter of refusing to believe, it is a matter of careful development of the Real Number Line. It can be proven that the real line is DENSE. This means that it has no holes. As mentioned it above posts, with out the irrationals and infinite length decimal representations we cannot fill the holes.

You need to separate the idea of an infinite decimal expansion and magnitude. Consider this.

Divide the interval from 0 to 1 into 10 boxes, now label each box with an integer 0 to 9, now take the last box (labeled 9) and subdivide it into 10 boxes, once again label 0 to 9. Now repeat this process as many times as you wish. Note that one end of all the boxes is anchored at 1 and never moves so all of your boxes contain numbers less then 1. You can repeat this process endlessly there are only 2 numbers which will never be enclosed in a box 1 because we defined it that way, and .999... because we can never get there, therefore we arrive at the conclusion that the 2 numbers which cannot be reached represent the same point on the number line.

For you to say .999... does not exist is to say that the above process of subdividing the line comes to an end, or that there is a largest integer clearly this is not true. Since there is no largest integer we can never complete the process of subdivision and we can never get .999... in a box that does not also contain the number 1. The proof linked in my sig shows that if I center boxes on 1 the number .999.... exists in EVERY box surrounding 1, there can only be 1 number that satisfies those conditions.

So infinite decimal expansions do indeed exist on the real line, this is a matter of proof and careful development, therefore knowledge not belief.

 

[zerocool1]

not this again