Is 1 = 0.9999......

[RossGr]

Since it has been made very clear over the past ~2yrs that you do not understand the basics of mathematics, yet presist in posting your nonsense.

You propose a number consisting of an infinite number of zeros ... followed by a one. Still not sure how and infinite number of something can be followed by something different. But on the other hand claimn that a simple infinitle long list of 9s cannot exist! By your definitions there can be no number with an infinite number of digits. I must ask, then what is the last digit? If there are not an infinite number of digits there must be a finite number. What is the last digit of PI or .999....

Your concept of a limited infinite is the source of all the troubles. As soon as you realize that when a Mathematician speaks of an infinte number of digits it is not the same as a very large finite number.

Why do I say you have a concept of a limited infinity, simply because you propose a number like .00...001 this with the infinite number of 0s followed by a 1. That 1 means that you are thinking of an end of infinity.

The real number .999.... has no end of the 9s there is no last 9.

once again you pick and choose the parts of my posts to respond to, you are all over the ad hominae attacks, trolls are pretty sensitive I guess. But totally ignore the fundamental math that also appears.

Why not respond to the fact that .00...001 + .999.... = 1 + .0000....999....

 

[HomeBrewerDude]

Here is a new rule:

You must read the entire thread before you reply



now maybe this thread will leave us in peace for the holidays.

 

[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.

 

[HomeBrewerDude]

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.

The sad part is that this mathematical proof is documented and explained in many places.
e.g., http://mathforum.org/dr.math/faq/faq.0.9999.html

 

[nmcglennon]

I think you should be clear... 0.999999...->infinity is not the same as 0.9999999999.

so 1 is not equal to 0.9999999999, but it is equal to 0.999999...->infinity.

 

[Kyteland]

Originally posted by: nmcglennon
I think you should be clear... 0.999999...->infinity is not the same as 0.9999999999.

so 1 is not equal to 0.9999999999, but it is equal to 0.999999...->infinity.

That's what the dots following the number mean. 0.9999..... != 0.9999. I don't think anyone missed the fact that the 9s repeat infinitely.

 

[HomeBrewerDude]

Originally posted by: Kyteland

Originally posted by: nmcglennon I think you should be clear... 0.999999...->infinity is not the same as 0.9999999999. so 1 is not equal to 0.9999999999, but it is equal to 0.999999...->infinity.

That's what the dots following the number mean. 0.9999..... != 0.9999. I don't think anyone missed the fact that the 9s repeat infinitely.

lol, i wouldn't be so sure.

 

[DrPizza]

1st hour is nearly up... no one's stepped forward to wager $100 yet.

I'll have to check later tonight... I could use an extra $100 for xmas

 

[HomeBrewerDude]

Originally posted by: DrPizza
1st hour is nearly up... no one's stepped forward to wager $100 yet. I'll have to check later tonight... I could use an extra $100 for xmas

You are preaching to the choir, but it would almost be worth $100 to see you do all that work.

 

[bleeb]

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.

0.9999..... doesn't EXACTLY equal 1. Think of it as one being a concept and the other finite and definite. THEY are NOT equal.

 

[MaxFusion16]

they are not the same
it doesn't matter if it approaches 1, it is NOT 1, just like an asymptote, the curve will approach a value, but it will NEVER reach that value. So therefore there will always be a difference, albeit infinitely small, but nevertheless conceptually they can't be the same.

 

[silverpig]

0.99999... -> infinity has absolutely no meaning.

That's like saying the limit of 2 is 3 as 2 approaches infinity. Makes no sense.


0.9r is taken to be 0.999... which is just short hand for a decimal point followed by an infinite string of nines. This has been spelled out numerous times in this thread already.

 

[silverpig]

Originally posted by: MaxFusion16
they are not the same
it doesn't matter if it approaches 1, it is NOT 1, just like an asymptote, the curve will approach a value, but it will NEVER reach that value. So therefore there will always be a difference, albeit infinitely small, but nevertheless conceptually they can't be the same.

0.999... is a number. How can a number approach something? Does 2 approach 3?

The sum 0.9 + 0.99 + 0.999 + ... is a series whose sum approaches 1. There will always be a difference. 0.9r is defined as the limit of this series. That limit is 1. 0.9r is NOT the series, but the LIMIT.

 

[MaxFusion16]

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.

your demonstration is flawed, consider this
does 2/7 really equal .285714285714285714285714285714285714285714285714285714... and 5/7 equal .714285714285714285714285714285714285714285714285714285...?
it's the same question, does 1/1 really equal 0.99999.................?
2/7 and 5/7 are 100% accurate values, there is no approximation, they are EXACT values, so therefore when added produce 1.
But you converted them into decimals, and repeating decimals are inherently inaccurate, because they are infinite. And we can't work with infinity, so eventually they get cut off and therefore produce errors, so when u add 2 repeating decimals together, naturally the result would have an error percentage, which causes it to not equate 1.
Remember back in high school when teachers asked u to always keep answers in fraction form until the last step then round?

 

[MaxFusion16]

Originally posted by: silverpig

Originally posted by: MaxFusion16
they are not the same
it doesn't matter if it approaches 1, it is NOT 1, just like an asymptote, the curve will approach a value, but it will NEVER reach that value. So therefore there will always be a difference, albeit infinitely small, but nevertheless conceptually they can't be the same.

0.999... is a number. How can a number approach something? Does 2 approach 3?

The sum 0.9 + 0.99 + 0.999 + ... is a series whose sum approaches 1. There will always be a difference. 0.9r is defined as the limit of this series. That limit is 1. 0.9r is NOT the series, but the LIMIT.

perhaps i used approach in the wrong context, but the point is they are 2 distinct values and therefore can't be equal.

 

[silverpig]

What about 4/2 and 2? They are two distinct values. Are they not equal?

 

[MaxFusion16]

Originally posted by: silverpig
What about 4/2 and 2? They are two distinct values. Are they not equal?

sure they are, 4/2 and 2 are both exact values with no approximation, they are just expressed differently. However, a repeating decimal is not exact.

 

[silverpig]

2 = 2.00000...

Is it not exact?

 

[MaxFusion16]

Originally posted by: silverpig
2 = 2.00000...

Is it not exact?

ok this is getting silly, if there is nothing other than 0s after the decimal point, then y even put the 0s there, it's just stupid. But if we are talking about significant figures, then no it's not exact, cuz significant figures is rounding, you are rounding the number to within an acceptable error percentage.

 

[Kyteland]

Man, my mailbox is getting hammered with so many subscription updates!

There are an infinite number of ways to represent an infinite amount of numbers. Is it so surprising that two different looking things can mean the same thing? 0.3333.... = 1/3 = .3+.03+.003+... = lots of differnt things.

"0.9999... doesn't look like 1" is not an argument for them not being the same. They are not obviously two distinct values. That is why we require a proof, not intuition.

 

[silverpig]

Originally posted by: MaxFusion16

Originally posted by: silverpig
2 = 2.00000...

Is it not exact?

ok this is getting silly, if there is nothing other than 0s after the decimal point, then y even put the 0s there, it's just stupid. But if we are talking about significant figures, then no it's not exact, cuz significant figures is rounding, you are rounding the number to within an acceptable error percentage.

The zeros are always there, we just don't write them. I was trying to illustrate that you're going about this without thinking about it. Look at this:

2.000... - 2.000... = 0.000...
1.000... - 0.999... = 0.000...

 

[MaxFusion16]

Originally posted by: Kyteland
Man, my mailbox is getting hammered with so many subscription updates!

There are an infinite number of ways to represent an infinite amount of numbers. Is it so surprising that two different looking things can mean the same thing? 0.3333.... = 1/3 = .3+.03+.003+... = lots of differnt things.

"0.9999... doesn't look like 1" is not an argument for them not being the same. They are not obviously two distinct values. That is why we require a proof, not intuition.

yes you are right, but the problem here is infinity. We can't work with infinity, so accuracy will always be limited, then there will always be some error to the real value.
In a perfect world, infinity exists...but we live no where near perfect. Fortunately there is walgreen...

 

[MaxFusion16]

Originally posted by: silverpig

Originally posted by: MaxFusion16

Originally posted by: silverpig
2 = 2.00000...

Is it not exact?

ok this is getting silly, if there is nothing other than 0s after the decimal point, then y even put the 0s there, it's just stupid. But if we are talking about significant figures, then no it's not exact, cuz significant figures is rounding, you are rounding the number to within an acceptable error percentage.

The zeros are always there, we just don't write them. I was trying to illustrate that you're going about this without thinking about it. Look at this:

2.000... - 2.000... = 0.000...
1.000... - 0.999... = 0.000...

did u not just disprove yourself?
if 1.00000 - 0.99999 = something, then 1 can't be equal to 0.99999 since there is something in between them.

 

[matt426malm]

Originally posted by: Kyteland
Man, my mailbox is getting hammered with so many subscription updates!

There are an infinite number of ways to represent an infinite amount of numbers. Is it so surprising that two different looking things can mean the same thing? 0.3333.... = 1/3 = .3+.03+.003+... = lots of differnt things.

"0.9999... doesn't look like 1" is not an argument for them not being the same. They are not obviously two distinct values. That is why we require a proof, not intuition.

This is perhaps a more simple example to understand 1/3 + 2/3 = 1 or .3333333... + .6666666... = .99999999... or 1 and there are no rounding errors with .333333333 it is perhaps confusing because this involves the concept of infinity. Infinity is not just a BIG number it is forever. It does get closer and closer so if you try the billionth digit it won't equal one; but it is infinity which is not a number.

 

[DrPizza]

Originally posted by: MaxFusion16

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.

your demonstration is flawed, consider this
does 2/7 really equal .285714285714285714285714285714285714285714285714285714... and 5/7 equal .714285714285714285714285714285714285714285714285714285...?
it's the same question, does 1/1 really equal 0.99999.................?
2/7 and 5/7 are 100% accurate values, there is no approximation, they are EXACT values, so therefore when added produce 1.
But you converted them into decimals, and repeating decimals are inherently inaccurate, because they are infinite. And we can't work with infinity, so eventually they get cut off and therefore produce errors, so when u add 2 repeating decimals together, naturally the result would have an error percentage, which causes it to not equate 1.
Remember back in high school when teachers asked u to always keep answers in fraction form until the last step then round?

AHHHHH, so you ADMIT that .9999... = 1. Wake up! Look at what I put in bold. Apparently you don't realize that we're talking about the INFINITELY long string of 9's. We never said anything about stopping it somewhere so that you can work with it in your calculator or computer. The error (the difference between .999... and 1) = 0 before you terminate the infinitely repeating decimal. The infinitely repeating decimal does indeed = 1. And, once you terminate it someplace, THEN it differs by 1x10^-n where n is the number of 9's in the truncated decimal. BUT, no one here thinks that the terminated decimal =1.

edit: ooops, missed a /b

2nd edit: Oh yeah, and I *am* one of those teachers in high school who tells you to wait until the last step to round.... that's because otherwise you would round 1/3 to .33 on the first step, multiply by 100, subtract 33, and insist the answer = 0 instead of 1/3.

Furthermore, for whoever it was a couple of posts back who said something about it "approaching infinity"
I agree! .3 + .03 + .003 + .0003 + . . . approaches 1/3 as you add more and more term. However, read these terms: the LIMIT of .3 + .03 + .003 + . . . *IS EQUAL TO 1/3*

Infinity is a difficult concept to grasp for some, and apparently cannot be grasped by others.