Saulbadguy

10-25-2006, 11:54 AM

http://en.wikipedia.org/wiki/0.999...

View Full Version : Does 0.999...=1?

Saulbadguy

10-25-2006, 11:54 AM

http://en.wikipedia.org/wiki/0.999...

noa

10-25-2006, 11:55 AM

Seems pretty obvious to me

SNR

10-25-2006, 11:59 AM

Do the Raiders suck?

NJ Chief Fan

10-25-2006, 11:59 AM

are we rounding numbers or something

Lzen

10-25-2006, 12:00 PM

My head hurts now.

SNR

10-25-2006, 12:01 PM

are we rounding numbers or somethingNo. If we were, then .50000...1 would equal 1 as well.

Stewie

10-25-2006, 12:02 PM

0.999... does equal 1. I remember that from high school calc class... oh, so many years ago.

Fish

10-25-2006, 12:04 PM

Interesting topic.......

If you're bored.... read more about it here....

http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

This will warp your brain....

If you're bored.... read more about it here....

http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

This will warp your brain....

SNR

10-25-2006, 12:04 PM

By the same logic....

What is the reciprocal of infinity?

What is the reciprocal of infinity?

Stewie

10-25-2006, 12:07 PM

By the same logic....

What is the reciprocal of infinity?

The number of wins the rai_ers had before AZ.

What is the reciprocal of infinity?

The number of wins the rai_ers had before AZ.

Rain Man

10-25-2006, 12:09 PM

These people are nuts. 0.999... approaches a limit of 1, and for all practical purposes it equals 1, but from a mathematical basis it doesn't equal 1. This is why we used to burn mathematicians in the Middle Ages.

Fish

10-25-2006, 12:11 PM

These people are nuts. 0.999... approaches a limit of 1, and for all practical purposes it equals 1, but from a mathematical basis it doesn't equal 1. This is why we used to burn mathematicians in the Middle Ages.

Check out some of the comments in the link I posted above.... Some serious nerd fights going on there.... it's quite humorous...

Nothing like math nerds talking smack over whether 0.999 = 1

Check out some of the comments in the link I posted above.... Some serious nerd fights going on there.... it's quite humorous...

Nothing like math nerds talking smack over whether 0.999 = 1

SNR

10-25-2006, 12:16 PM

Check out some of the comments in the link I posted above.... Some serious nerd fights going on there.... it's quite humorous...

Nothing like math nerds talking smack over whether 0.999 = 1Yo momma so stupid she couldn't solve single-variable equations if someone hit her with a TI-91 calculator

Nothing like math nerds talking smack over whether 0.999 = 1Yo momma so stupid she couldn't solve single-variable equations if someone hit her with a TI-91 calculator

milkman

10-25-2006, 12:21 PM

The more imprtant question here is this:

Who the **** cares?

Who the **** cares?

banyon

10-25-2006, 12:29 PM

These people are nuts. 0.999... approaches a limit of 1, and for all practical purposes it equals 1, but from a mathematical basis it doesn't equal 1. This is why we used to burn mathematicians in the Middle Ages.

This is exactly right. It reminds me of Zeno's Paradoxes (http://en.wikipedia.org/wiki/Xeno%27s_paradox).

This is exactly right. It reminds me of Zeno's Paradoxes (http://en.wikipedia.org/wiki/Xeno%27s_paradox).

DaFace

10-25-2006, 12:35 PM

That's weird. It may be infinitely close to one, but it isn't actually EQUAL to one IMO.

'Hamas' Jenkins

10-25-2006, 12:49 PM

While there are such things as real and imaginary numbers, numbers aren't real, they are just a mathematical construct. Even though it defies conventional logic, I have to concur that .999=1 because of the artifice of the system in question as well as the nature of infinity.

Fish

10-25-2006, 12:53 PM

Yo momma so stupid she couldn't solve single-variable equations if someone hit her with a TI-91 calculator

Yeah? Well yo momma so dumb, she think π = 8 slices.

Yeah? Well yo momma so dumb, she think π = 8 slices.

milkman

10-25-2006, 12:56 PM

I'm surrounded by nerds.

DaFace

10-25-2006, 01:00 PM

While there are such things as real and imaginary numbers, numbers aren't real, they are just a mathematical construct. Even though it defies conventional logic, I have to concur that .999=1 because of the artifice of the system in question as well as the nature of infinity.

Infinite decimals, in my opinion, are never EQUAL to fractions, IMO. Most of the proofs I've seen revolve around the idea that 1/3 = .333... or similar fractions. I'd contend that that is not true either. .333... is APPROXIMATELY equal to 1/3, but not exactly.

On the other hand, I don't really care that much one way or another.

Infinite decimals, in my opinion, are never EQUAL to fractions, IMO. Most of the proofs I've seen revolve around the idea that 1/3 = .333... or similar fractions. I'd contend that that is not true either. .333... is APPROXIMATELY equal to 1/3, but not exactly.

On the other hand, I don't really care that much one way or another.

tiptap

10-25-2006, 01:00 PM

Think of repeating .9999999 as a process. 1 as a static count. Since the process is a calculus question and we can determine the limit of such a process, then repeating .999999 is equal to 1 in the completion of the process.

Dr. Van Halen

10-25-2006, 01:03 PM

While there are such things as real and imaginary numbers, numbers aren't real, they are just a mathematical construct. Even though it defies conventional logic, I have to concur that .999=1 because of the artifice of the system in question as well as the nature of infinity.

Because of the silliness of math/artiface of the question, then yes. 1/3 + 2/3 = 1, therefore .3repeating + .6repeating must equal 1.

The nature of infinity, on the other hand, suggests just the opposite. Infinity is a concept that cannot be manipulated by mathematical constructs. It is oversimplistic to state that infinity divided by itself is 1.

Because of the silliness of math/artiface of the question, then yes. 1/3 + 2/3 = 1, therefore .3repeating + .6repeating must equal 1.

The nature of infinity, on the other hand, suggests just the opposite. Infinity is a concept that cannot be manipulated by mathematical constructs. It is oversimplistic to state that infinity divided by itself is 1.

'Hamas' Jenkins

10-25-2006, 01:04 PM

Infinite decimals, in my opinion, are never EQUAL to fractions, IMO. Most of the proofs I've seen revolve around the idea that 1/3 = .333... or similar fractions. I'd contend that that is not true either. .333... is APPROXIMATELY equal to 1/3, but not exactly.

On the other hand, I don't really care that much one way or another.

This has to do with the fallibility of signs and signifiers. There is no such thing as "1" just as there is no such thing as "1/3". They are representations of a concept, but nothing more or nothing less. We give the concept credence because it helps to order and explain our world, even though it is fallible. We have no way to numerically represent the square root of -1, so we use "i" which is another sign that really doesn't mean anything tangibly. That doesn't mean that the concept of numbers is ridiculous or shouldn't be used, just that it is imperfect.

On the other hand, I don't really care that much one way or another.

This has to do with the fallibility of signs and signifiers. There is no such thing as "1" just as there is no such thing as "1/3". They are representations of a concept, but nothing more or nothing less. We give the concept credence because it helps to order and explain our world, even though it is fallible. We have no way to numerically represent the square root of -1, so we use "i" which is another sign that really doesn't mean anything tangibly. That doesn't mean that the concept of numbers is ridiculous or shouldn't be used, just that it is imperfect.

'Hamas' Jenkins

10-25-2006, 01:06 PM

Because of the silliness of math/artiface of the question, then yes. 1/3 + 2/3 = 1, therefore .3repeating + .6repeating must equal 1.

The nature of infinity, on the other hand, suggests just the opposite. Infinity is a concept that cannot be manipulated by mathematical constructs. It is oversimplistic to state that infinity divided by itself is 1.

You are misinterpreting my post. I was using infinity as an analogy to explain the imperfect nature of numbers, not a way to get to "1" so to speak.

The nature of infinity, on the other hand, suggests just the opposite. Infinity is a concept that cannot be manipulated by mathematical constructs. It is oversimplistic to state that infinity divided by itself is 1.

You are misinterpreting my post. I was using infinity as an analogy to explain the imperfect nature of numbers, not a way to get to "1" so to speak.

tiptap

10-25-2006, 01:10 PM

Because of the silliness of math/artiface of the question, then yes. 1/3 + 2/3 = 1, therefore .3repeating + .6repeating must equal 1.

The nature of infinity, on the other hand, suggests just the opposite. Infinity is a concept that cannot be manipulated by mathematical constructs. It is oversimplistic to state that infinity divided by itself is 1.

There are different forms of infinity. For example there is greater real numbers between 0 and 1 than all counting numbers. This can be shown by noting there is no one operation that connects counting numbers to all real numbers between 0 and 1. You need lots of different operations to match up numbers and even then transcendental numbers between 0 and 1 can be unrepresented.

As such there are processes of infinity, well defined, that can be manuplilated well mathematically. That is what Calculus is all about. However the reasoning isn't explored so much in Calculus classes. That is reserved for Inductive Methods classes.

The nature of infinity, on the other hand, suggests just the opposite. Infinity is a concept that cannot be manipulated by mathematical constructs. It is oversimplistic to state that infinity divided by itself is 1.

There are different forms of infinity. For example there is greater real numbers between 0 and 1 than all counting numbers. This can be shown by noting there is no one operation that connects counting numbers to all real numbers between 0 and 1. You need lots of different operations to match up numbers and even then transcendental numbers between 0 and 1 can be unrepresented.

As such there are processes of infinity, well defined, that can be manuplilated well mathematically. That is what Calculus is all about. However the reasoning isn't explored so much in Calculus classes. That is reserved for Inductive Methods classes.

vailpass

10-25-2006, 01:14 PM

"Does 0.999...=1?"

When buying hamburger sure, that's close enough.

When picking up a recreational drug of choice .999 is definetely NOT 1.

When buying hamburger sure, that's close enough.

When picking up a recreational drug of choice .999 is definetely NOT 1.

listopencil

10-25-2006, 01:16 PM

No.

tyton75

10-25-2006, 01:43 PM

Why wouldn't infinity divided by infinity equal 1?

Ogre, "what if C. A. T. really spelled DOG?"

Ogre, "what if C. A. T. really spelled DOG?"

ck_IN

10-25-2006, 01:52 PM

That would be a big no.

F(x) = .9999 almost = 1 as the limit of x approaches infinity but it never exactly equals 1 since x never exactly equals infinity.

F(x) = .9999 almost = 1 as the limit of x approaches infinity but it never exactly equals 1 since x never exactly equals infinity.

'Hamas' Jenkins

10-25-2006, 02:12 PM

Why wouldn't infinity divided by infinity equal 1?

Ogre, "what if C. A. T. really spelled DOG?"

Because infinity isn't finite :drool:

Ogre, "what if C. A. T. really spelled DOG?"

Because infinity isn't finite :drool:

'Hamas' Jenkins

10-25-2006, 02:14 PM

That would be a big no.

F(x) = .9999 almost = 1 as the limit of x approaches infinity but it never exactly equals 1 since x never exactly equals infinity.

:spock:

Students of mathematics often reject the equality of 0.999… and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:

* Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.[11]

* Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity."[12]

* Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since the sequence never reaches its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.[13]

* Some students regard 0.999... as having a fixed value which is less than 1 but by an infinitely small amount. (This is a more sophisticated response.)

These ideas are mistaken in the context of the standard real numbers, although many of them are partially borne out in more sophisticated structures, either invented for their general mathematical utility or as instructive counterexamples to better understand 0.999….

F(x) = .9999 almost = 1 as the limit of x approaches infinity but it never exactly equals 1 since x never exactly equals infinity.

:spock:

Students of mathematics often reject the equality of 0.999… and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:

* Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.[11]

* Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity."[12]

* Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since the sequence never reaches its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.[13]

* Some students regard 0.999... as having a fixed value which is less than 1 but by an infinitely small amount. (This is a more sophisticated response.)

These ideas are mistaken in the context of the standard real numbers, although many of them are partially borne out in more sophisticated structures, either invented for their general mathematical utility or as instructive counterexamples to better understand 0.999….

Baby Lee

10-25-2006, 02:25 PM

There are no synonyms in a closed numerical system.

If there is NO difference between .99.... and 1, there is likewise no difference between .99......8 and .99....., and no difference between .99......7 and .99.....8, and so on.

If there is NO difference between .99.... and 1, there is likewise no difference between .99......8 and .99....., and no difference between .99......7 and .99.....8, and so on.

ct

10-25-2006, 02:29 PM

By the same logic....

What is the reciprocal of infinity?

NULL

What is the reciprocal of infinity?

NULL

tiptap

10-25-2006, 02:46 PM

There are no synonyms in a closed numerical system.

If there is NO difference between .99.... and 1, there is likewise no difference between .99......8 and .99....., and no difference between .99......7 and .99.....8, and so on.

Is this why you are a lawyer and not a mathematician or scientist. You have moved the question to a semantic domain to answer a mathematical question. We are not talking about .9999. We are talking about a repeating .99999999999. . . And just like a number cannot be represented exactly in base hexadecimal as well as in decimal (and vice versa) the repeating .99999999. . . is the same as 1. As stated earlier by someone, the decimal representation of one third is repeating .3333. . . and two thirds .6666. . . and added together both have to equal one. The repeating symbol, usually a bar over the repeating digits, is a operator and that operation is a well defined function that for every epsilon in the range there exists an arbitrary percision of delta in the domain that assures that this is a well behaved operation. The limit of which is .99999 repeating is equal to 1.

If there is NO difference between .99.... and 1, there is likewise no difference between .99......8 and .99....., and no difference between .99......7 and .99.....8, and so on.

Is this why you are a lawyer and not a mathematician or scientist. You have moved the question to a semantic domain to answer a mathematical question. We are not talking about .9999. We are talking about a repeating .99999999999. . . And just like a number cannot be represented exactly in base hexadecimal as well as in decimal (and vice versa) the repeating .99999999. . . is the same as 1. As stated earlier by someone, the decimal representation of one third is repeating .3333. . . and two thirds .6666. . . and added together both have to equal one. The repeating symbol, usually a bar over the repeating digits, is a operator and that operation is a well defined function that for every epsilon in the range there exists an arbitrary percision of delta in the domain that assures that this is a well behaved operation. The limit of which is .99999 repeating is equal to 1.

ck_IN

10-25-2006, 02:48 PM

<i>Some students regard 0.999... as having a fixed value which is less than 1 but by an infinitely small amount.</i>

I guess I would fall in this camp Hamas.

<i>If they accept an infinite string of nines, they may still expect a last 9 "at infinity.</i>

And that is how the concept of mathematical infinity was drilled into us while getting my Math degree.

.999... may approach 1 but it will never get there because there will always be one last 9 and 1-.99... will never equal zero.

Think of it this way: If someone were to hand you 100 dollar bills or 99 dollar bills and 99 cents, which would you take? If .99... truely equaled 1 then your choice wouldn't matter. I bet I know which you'd take.

I guess I would fall in this camp Hamas.

<i>If they accept an infinite string of nines, they may still expect a last 9 "at infinity.</i>

And that is how the concept of mathematical infinity was drilled into us while getting my Math degree.

.999... may approach 1 but it will never get there because there will always be one last 9 and 1-.99... will never equal zero.

Think of it this way: If someone were to hand you 100 dollar bills or 99 dollar bills and 99 cents, which would you take? If .99... truely equaled 1 then your choice wouldn't matter. I bet I know which you'd take.

jlscorpio

10-25-2006, 02:50 PM

So this means that ALL players are using 'roids???

ck_IN

10-25-2006, 02:52 PM

<i>So this means that ALL players are using 'roids???</i>

Only as f(x) = team as the limit of x approaches SD or Denver.

Only as f(x) = team as the limit of x approaches SD or Denver.

cdcox

10-25-2006, 03:02 PM

This pretty much nails it (from the Wikipedia site):

One reason that infinite decimals are a necessary extension of finite decimals is to represent fractions. Using long division, a simple division of integers like 1⁄3 becomes a recurring decimal, 0.333…, in which the digits repeat without end. This decimal yields a quick proof for 0.999… = 1. Multiplication of 3 times 3 produces 9 in each digit, so 3 × 0.333… equals 0.999…. But 3 × 1⁄3 equals 1, so 0.999… = 1.[1] Another form of this proof multiplies 1/9 = 0.111… by 9.

One reason that infinite decimals are a necessary extension of finite decimals is to represent fractions. Using long division, a simple division of integers like 1⁄3 becomes a recurring decimal, 0.333…, in which the digits repeat without end. This decimal yields a quick proof for 0.999… = 1. Multiplication of 3 times 3 produces 9 in each digit, so 3 × 0.333… equals 0.999…. But 3 × 1⁄3 equals 1, so 0.999… = 1.[1] Another form of this proof multiplies 1/9 = 0.111… by 9.

tiptap

10-25-2006, 03:04 PM

<i>Some students regard 0.999... as having a fixed value which is less than 1 but by an infinitely small amount.</i>

I guess I would fall in this camp Hamas.

<i>If they accept an infinite string of nines, they may still expect a last 9 "at infinity.</i>

And that is how the concept of mathematical infinity was drilled into us while getting my Math degree.

.999... may approach 1 but it will never get there because there will always be one last 9 and 1-.99... will never equal zero.

Think of it this way: If someone were to hand you 100 dollar bills or 99 dollar bills and 99 cents, which would you take? If .99... truely equaled 1 then your choice wouldn't matter. I bet I know which you'd take.

This seems to be a scientists approach to Calculus. One that is valid for large numbers or in this case a large number of repeating digits. But I think in this case that the repeating .999999 is exactly equal to one. The logical structure that allows for decimal representation does not allow for a finite representation of all numbers. But we have invented the symbolism that represents in decimal system and allows for the transition from a decimal system to a counting system.

I guess I would fall in this camp Hamas.

<i>If they accept an infinite string of nines, they may still expect a last 9 "at infinity.</i>

And that is how the concept of mathematical infinity was drilled into us while getting my Math degree.

.999... may approach 1 but it will never get there because there will always be one last 9 and 1-.99... will never equal zero.

Think of it this way: If someone were to hand you 100 dollar bills or 99 dollar bills and 99 cents, which would you take? If .99... truely equaled 1 then your choice wouldn't matter. I bet I know which you'd take.

This seems to be a scientists approach to Calculus. One that is valid for large numbers or in this case a large number of repeating digits. But I think in this case that the repeating .999999 is exactly equal to one. The logical structure that allows for decimal representation does not allow for a finite representation of all numbers. But we have invented the symbolism that represents in decimal system and allows for the transition from a decimal system to a counting system.

'Hamas' Jenkins

10-25-2006, 03:10 PM

<i>Some students regard 0.999... as having a fixed value which is less than 1 but by an infinitely small amount.</i>

I guess I would fall in this camp Hamas.

<i>If they accept an infinite string of nines, they may still expect a last 9 "at infinity.</i>

And that is how the concept of mathematical infinity was drilled into us while getting my Math degree.

.999... may approach 1 but it will never get there because there will always be one last 9 and 1-.99... will never equal zero.

Think of it this way: If someone were to hand you 100 dollar bills or 99 dollar bills and 99 cents, which would you take? If .99... truely equaled 1 then your choice wouldn't matter. I bet I know which you'd take.

You are trying to impose a finite system on an infinite concept. It doesn't work that way.

I guess I would fall in this camp Hamas.

<i>If they accept an infinite string of nines, they may still expect a last 9 "at infinity.</i>

And that is how the concept of mathematical infinity was drilled into us while getting my Math degree.

.999... may approach 1 but it will never get there because there will always be one last 9 and 1-.99... will never equal zero.

Think of it this way: If someone were to hand you 100 dollar bills or 99 dollar bills and 99 cents, which would you take? If .99... truely equaled 1 then your choice wouldn't matter. I bet I know which you'd take.

You are trying to impose a finite system on an infinite concept. It doesn't work that way.

Baby Lee

10-25-2006, 03:19 PM

Is this why you are a lawyer and not a mathematician or scientist. You have moved the question to a semantic domain to answer a mathematical question. We are not talking about .9999. We are talking about a repeating .99999999999. . .

I know the distinction, that's why I used the '....'

1 is a straight line, and .999..... is an arc that comes more closely, and more closely to both intersecting and paralleling that line, while doing neither through an infinite travel.

[Very] roughly denoted in the pic attached.

So if 1 and .9 start at opposite ends of the universe, with the '1' line extending forever, and the '.9999.....' refining itself infinitely as '9s' are added to the end of the decimal, the '.9999.....' arc will never intersect AND never parallel, the 1 line.

Edit: BTW: I haven't read the links in this post, so if no one else has expressed the concept in these terms [though I'm sure someone somewhere has], I call dibs.

I know the distinction, that's why I used the '....'

1 is a straight line, and .999..... is an arc that comes more closely, and more closely to both intersecting and paralleling that line, while doing neither through an infinite travel.

[Very] roughly denoted in the pic attached.

So if 1 and .9 start at opposite ends of the universe, with the '1' line extending forever, and the '.9999.....' refining itself infinitely as '9s' are added to the end of the decimal, the '.9999.....' arc will never intersect AND never parallel, the 1 line.

Edit: BTW: I haven't read the links in this post, so if no one else has expressed the concept in these terms [though I'm sure someone somewhere has], I call dibs.

SNR

10-25-2006, 03:29 PM

There are no synonyms in a closed numerical system.

If there is NO difference between .99.... and 1, there is likewise no difference between .99......8 and .99....., and no difference between .99......7 and .99.....8, and so on.These are irrational numbers though. They're real numbers, but they're irrational. .999...8 doesn't exist because when will the 8 be reached? If .999... = c and .999....8 = b, the only reason we make differences between c and 1 and not c and b is because c and 1 are compared because c is either 1 or not 1.

If there is NO difference between .99.... and 1, there is likewise no difference between .99......8 and .99....., and no difference between .99......7 and .99.....8, and so on.These are irrational numbers though. They're real numbers, but they're irrational. .999...8 doesn't exist because when will the 8 be reached? If .999... = c and .999....8 = b, the only reason we make differences between c and 1 and not c and b is because c and 1 are compared because c is either 1 or not 1.

morphius

10-25-2006, 03:35 PM

Does this also mean that we have an infinitie numbers that equal 1, cause you have to think that .9999999999999999999998.... repeated to infinity isn't much off either.

banyon

10-25-2006, 03:38 PM

1 > 0.999999999999999999999999999999...

banyon

10-25-2006, 03:39 PM

Rainman got it right when he said it's a practical construct, but the concepts are not equivalent, which is what the numbers are supposed to represent.

SNR

10-25-2006, 03:43 PM

Does this also mean that we have an infinitie numbers that equal 1, cause you have to think that .9999999999999999999998.... repeated to infinity isn't much off either.

These are irrational numbers though. They're real numbers, but they're irrational. .999...8 doesn't exist because when will the 8 be reached? If .999... = c and .999....8 = b, the only reason we make differences between c and 1 and not c and b is because c and 1 are compared because c is either 1 or not 1.

These are irrational numbers though. They're real numbers, but they're irrational. .999...8 doesn't exist because when will the 8 be reached? If .999... = c and .999....8 = b, the only reason we make differences between c and 1 and not c and b is because c and 1 are compared because c is either 1 or not 1.

Predarat

10-25-2006, 03:52 PM

But what does .9991 equal?

cdcox

10-25-2006, 04:00 PM

I'l say it again:

1/3 = 0.33333....

3*0.3333... = 0.9999....

3*1/3 = 1

0.9999.... = 1

Either the fourth statement is true or one of the preceding statements is false. You can't have it both ways..

1/3 = 0.33333....

3*0.3333... = 0.9999....

3*1/3 = 1

0.9999.... = 1

Either the fourth statement is true or one of the preceding statements is false. You can't have it both ways..

Baby Lee

10-25-2006, 04:05 PM

I'l say it again:

1/3 = 0.33333....

3*0.3333... = 0.9999....

3*1/3 = 1

0.9999.... = 1

Either the fourth statement is true or one of the preceding statements is false. You can't have it both ways..

The first is false, as the shorthand of 1/3 is a concept that is not completely reproduced by .333...

The same straight line/arc approximation that you have with 1 and .999... applies.

1/3 = 0.33333....

3*0.3333... = 0.9999....

3*1/3 = 1

0.9999.... = 1

Either the fourth statement is true or one of the preceding statements is false. You can't have it both ways..

The first is false, as the shorthand of 1/3 is a concept that is not completely reproduced by .333...

The same straight line/arc approximation that you have with 1 and .999... applies.

banyon

10-25-2006, 04:06 PM

I'l say it again:

1/3 = 0.33333....

3*0.3333... = 0.9999....

3*1/3 = 1

0.9999.... = 1

Either the fourth statement is true or one of the preceding statements is false. You can't have it both ways..

1/3 is a fraction, not a whole integer. None of your premises equate nominally incomplete integers with whole integers, so they would be disanalogous.

1/3 = 0.33333....

3*0.3333... = 0.9999....

3*1/3 = 1

0.9999.... = 1

Either the fourth statement is true or one of the preceding statements is false. You can't have it both ways..

1/3 is a fraction, not a whole integer. None of your premises equate nominally incomplete integers with whole integers, so they would be disanalogous.

Baby Lee

10-25-2006, 04:10 PM

1/3 is a fraction, not a whole integer. None of your premises equate nominally incomplete integers with whole integers, so they would be disanalogous.

I'm dying to know, for you math brainiacs, has anyone expressed to quandry as I have, in terms of a line and ever approximating arc?

I'm dying to know, for you math brainiacs, has anyone expressed to quandry as I have, in terms of a line and ever approximating arc?

PastorMikH

10-25-2006, 04:12 PM

If you are talking currency it does - at the gas pump they always round up - gas price is 2.099 you end up paying 2.30 for it. However, in regards to mass, if an oject were to weigh .99999 lb and another object were to weigh 1 lb, if the scale were acurate enough, it would tilt in the direction of the 1.

I think what this is in reality, either is a therom that some grad student thought up to get his degree or a prophesor thought up to get his government funding.:)

I think what this is in reality, either is a therom that some grad student thought up to get his degree or a prophesor thought up to get his government funding.:)

cdcox

10-25-2006, 04:14 PM

So now 1/3 does not equal 0.333... LMAO

Ok, try to disprove this one:

assertion 10 × 0.999… = 9.999…

assertion c = 0.999…

step 1 10c = 9.999…

step 2 10c - c = 9.999… − 0.999…

step 3 9c = 9

proof c = 1

Ok, try to disprove this one:

assertion 10 × 0.999… = 9.999…

assertion c = 0.999…

step 1 10c = 9.999…

step 2 10c - c = 9.999… − 0.999…

step 3 9c = 9

proof c = 1

cdcox

10-25-2006, 04:17 PM

I'm dying to know, for you math brainiacs, has anyone expressed to quandry as I have, in terms of a line and ever approximating arc?

The problem here is that 0.9999... is not expressed by any point on your arc. As soon as you select a point on you arc, you've turncated the series and the equality fails.

The problem here is that 0.9999... is not expressed by any point on your arc. As soon as you select a point on you arc, you've turncated the series and the equality fails.

Logical

10-25-2006, 04:23 PM

The problem is that .66666666666666666666666666666666 does not equal 2/3 it only approximates it.

cdcox

10-25-2006, 04:24 PM

The problem is that .66666666666666666666666666666666 does not equal 2/3 it only approximates it.

Agreed. But 0.66666666666666666666666666666666... does equal 2/3.

Agreed. But 0.66666666666666666666666666666666... does equal 2/3.

Baby Lee

10-25-2006, 04:26 PM

The problem here is that 0.9999... is not expressed by any point on your arc. As soon as you select a point on you arc, you've turncated the series and the equality fails.

No, it's an ever continuing arc, that neither intersects or parallels, though it infinitely closer approximates both intersection AND parallel.

They start out at points on opposite sides of the universe, and eventually ride tracks separated on a subatomic level and as near parallel as to be unmeasurable.

No, it's an ever continuing arc, that neither intersects or parallels, though it infinitely closer approximates both intersection AND parallel.

They start out at points on opposite sides of the universe, and eventually ride tracks separated on a subatomic level and as near parallel as to be unmeasurable.

Logical

10-25-2006, 04:27 PM

Agreed. But 0.66666666666666666666666666666666... does equal 2/3.No, not in my advanced college mathmatics it did not. Just like Pi is not really an exact calculation for a circles circumference, only an approximation.

'Hamas' Jenkins

10-25-2006, 04:31 PM

At it's heart, this is a debate between realism and nominalism.

StcChief

10-25-2006, 04:36 PM

Developing software code in JAVA, VB, etc.

the math libraries derive a value may have .99999999

but compares to 1 of variables :var fail :banghead:

So you must stick a ROUND(:var) in code

You figure out the advantage. Fuzzy math. :banghead:

the math libraries derive a value may have .99999999

but compares to 1 of variables :var fail :banghead:

So you must stick a ROUND(:var) in code

You figure out the advantage. Fuzzy math. :banghead:

Baby Lee

10-25-2006, 04:46 PM

Developing software code in JAVA, VB, etc.

the math libraries derive a value may have .99999999

but compares to 1 of variables :var fail :banghead:

So you must stick a ROUND(:var) in code

You figure out the advantage. Fuzzy math. :banghead:

Peter, Samir, and Michael Bolton [not that faig], just had an idea to make $$ millions!!!

the math libraries derive a value may have .99999999

but compares to 1 of variables :var fail :banghead:

So you must stick a ROUND(:var) in code

You figure out the advantage. Fuzzy math. :banghead:

Peter, Samir, and Michael Bolton [not that faig], just had an idea to make $$ millions!!!

tiptap

10-25-2006, 04:48 PM

I'm dying to know, for you math brainiacs, has anyone expressed to quandry as I have, in terms of a line and ever approximating arc?

Actually your geometric rendetion is the discussion of the arbitrariness of Euclid's Geometry that parallel lines never meet. Some Greek fellow used the hyperbolic line, that is what you are drawing, as a counter example to the parallel line axiom.

Actually your geometric rendetion is the discussion of the arbitrariness of Euclid's Geometry that parallel lines never meet. Some Greek fellow used the hyperbolic line, that is what you are drawing, as a counter example to the parallel line axiom.

JBucc

10-25-2006, 04:50 PM

Actually your geometric rendetion is the discussion of the arbitrariness of Euclid's Geometry that parallel lines never meet. Some Greek fellow used the hyperbolic line, that is what you are drawing, as a counter example to the parallel line axiom.I think my brain just esploded

Thig Lyfe

10-25-2006, 04:53 PM

Weird. Shouldn't we be talking about poop or something?

DanT

10-25-2006, 04:53 PM

The unit number has two decimal expansions, 0.999... and 1.000... . Indeed, there are two expansions for any real number x in a base-n system (n a positive integer), when x=m/n and m is an integer. In base-2, the unit number can be represented as 1.000... or 0.111... .

DanT (Ph.D. in Math)

DanT (Ph.D. in Math)

JBucc

10-25-2006, 04:59 PM

Here's my thoughts, it's got a . in front and something with a . in front can't be the same as something without a . in front.

JBucc (on the honor roll in 6th grade)

JBucc (on the honor roll in 6th grade)

DanT

10-25-2006, 05:00 PM

Agreed. But 0.66666666666666666666666666666666... does equal 2/3.

Exactly.

In base-3, though, the number 2/3 can be represented by either

0.2000...

or

0.1222... .

;)

Exactly.

In base-3, though, the number 2/3 can be represented by either

0.2000...

or

0.1222... .

;)

cdcox

10-25-2006, 05:02 PM

Suppose you want to estimate 1 with a series of "n" 9's.

1-1/10 = 0.9

1-1/100 = 0.99

1-1/1000 = 0.999

The general formula is:

1-1/10^n

the limit of 1/10^n as n goes to infinity is zero.

Note that in all of your math classes you used equal signs for all of these relationships, not approximately equal to.

1-1/10 = 0.9

1-1/100 = 0.99

1-1/1000 = 0.999

The general formula is:

1-1/10^n

the limit of 1/10^n as n goes to infinity is zero.

Note that in all of your math classes you used equal signs for all of these relationships, not approximately equal to.

Logical

10-25-2006, 05:04 PM

Exactly.

In base-3, though, the number 2/3 can be represented by either

0.2000...

or

0.1222... .

;)

Though fundamentally I believe we can disagree, I would never argue Math with DanT.:p

In base-3, though, the number 2/3 can be represented by either

0.2000...

or

0.1222... .

;)

Though fundamentally I believe we can disagree, I would never argue Math with DanT.:p

cdcox

10-25-2006, 05:05 PM

The unit number has two decimal expansions, 0.999... and 1.000... . Indeed, there are two expansions for any real number x in a base-n system (n a positive integer), when x=m/n and m is an integer. In base-2, the unit number can be represented as 1.000... or 0.111... .

DanT (Ph.D. in Math)

Yeah, the cavalry is here!

DanT (Ph.D. in Math)

Yeah, the cavalry is here!

DanT

10-25-2006, 05:06 PM

Looking through that Wikipedia article, the argument that I find the most congenial is entitled "Nested intervals and least upper bounds". The least upper bounds property ("any nonempty set of real numbers that is bounded above has a least upper bound") is very deep. It's what separates real numbers from rational numbers. For example, there is no rational number that is the least upper bound for the set of all positive rational numbers less than the square root of 2.

DanT

10-25-2006, 05:09 PM

Though fundamentally I believe we can disagree, I would never argue Math with DanT.:p

You shouldn't give me that much credit. There's tons of math that I don't know that well, like differential equations, for example. I do know more than most about real numbers, though, because Real Analysis was my minor. My major was Probability and Statistics.

You shouldn't give me that much credit. There's tons of math that I don't know that well, like differential equations, for example. I do know more than most about real numbers, though, because Real Analysis was my minor. My major was Probability and Statistics.

StcChief

10-25-2006, 05:33 PM

The .9999 comes up on every project I'm on eventually

Wierd. Java, C#, VB, whatever client tool.

if the value comes from client application I don't trust it.

Wierd. Java, C#, VB, whatever client tool.

if the value comes from client application I don't trust it.

Rain Man

10-25-2006, 05:34 PM

I agree with cdcox and dant....whatever they said.

DanT

10-25-2006, 05:41 PM

The .9999 comes up on every project I'm on eventually

Wierd. Java, C#, VB, whatever client tool.

if the value comes from client application I don't trust it.

The annoyance of round-off errors is briefly talked about in the Wikipedia article on Numerical Analysis:

http://en.wikipedia.org/wiki/Numerical_analysis

Wierd. Java, C#, VB, whatever client tool.

if the value comes from client application I don't trust it.

The annoyance of round-off errors is briefly talked about in the Wikipedia article on Numerical Analysis:

http://en.wikipedia.org/wiki/Numerical_analysis

StcChief

10-25-2006, 05:42 PM

Weird. Shouldn't we be talking about poop or something?

There is a poop thread with your name on it

go find it.

:p

There is a poop thread with your name on it

go find it.

:p

Saulbadguy

10-25-2006, 06:06 PM

I love this topic. It always draws out the intellectuals. ;)

JBucc

10-25-2006, 06:07 PM

I love this topic. It always draws out the intellectuals. ;)You don't have to draw me out I'm always here.

SNR

10-25-2006, 06:55 PM

I love this topic. It always draws out the intellectuals. ;)I certainly haven't seen the likes of Halfcan 'round these parts yet...

beavis

10-25-2006, 07:37 PM

What a bunch of Nerds.

BTW, I agree with Rainman, it approaches 1, but is not equal to it. At least, I think that's what I remember from Calc II.

BTW, I agree with Rainman, it approaches 1, but is not equal to it. At least, I think that's what I remember from Calc II.

Bob Dole

10-25-2006, 07:46 PM

Bob Dole is fairly certain that anything in excess of .51 is equal to 1.

It's far too complicated to put together any sort of proof, and we can't risk a student feeling bad about his or herself by getting the answer wrong.

It's far too complicated to put together any sort of proof, and we can't risk a student feeling bad about his or herself by getting the answer wrong.

listopencil

10-25-2006, 11:20 PM

Infinity is an artificial concept. We can't actually point to anything and declare it to be infinite. The concept of "one" is fairly easy to demonstrate and farly easy to understand. Within my understanding of what "infinite" means I don't believe the two numbers are equal.

Archie F. Swin

10-25-2006, 11:29 PM

marcus welby

TinyEvel

10-26-2006, 12:17 AM

YES! Don't overthink it. I'm SICKof mutherfriggin' cheapskates who overthink it!

WTF is this, Tijuana??!!

WTF is this, Tijuana??!!

PastorMikH

10-26-2006, 12:20 AM

YES! Don't overthink it. I'm SICKof mutherfriggin' cheapskates who overthink it!

WTF is this, Tijuana??!!

FWIW, in Tijuana, the difference between .9999 and 1.0 is probably about 6 pesos.

:)

WTF is this, Tijuana??!!

FWIW, in Tijuana, the difference between .9999 and 1.0 is probably about 6 pesos.

:)

TinyEvel

10-26-2006, 12:23 AM

FWIW, in Tijuana, the difference between .9999 and 1.0 is probably about 6 pesos.

:)

ROFL

VIVA MEJICO!!!

:)

ROFL

VIVA MEJICO!!!

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