lol...check out the front-page article on wikipedia

[RapidSnail]

Originally posted by: jman19

Originally posted by: jbourne77

Originally posted by: The Green Bean

Originally posted by: jbourne77

Originally posted by: The Green Bean

Originally posted by: jbourne77

Originally posted by: The Green Bean
.99999...is not eual to one. Its 1 - 0.000000000......1

Sadly, dumb people will never realize that mere earthlings will NEVER be able to grasp the concept of infinity.

Speaking of dumb people, dumbass, "0.000000000......1" is not even a number. It's no more a number than 1.0.0.03.0.3.dkx.33.Qfuck.03 is a number. It's just an arbitrary arrangement of characters that you've thrown together in a vein attempt to make others look less intelligent than yourself, when in fact, you've proven - quite well, I might add - just the opposite.

The "1" never comes into play. You've already stated there is an infinite number of 0's and, as such, you've already defined 0 for the place value wherever which you think 1 resides. Infinity is forever. You don't just waltz to the end of it and slap a 1 on for good measure.

In short, 0.000... is ALWAYS, without question, ZERO.
0.000...x is ALWAYS, without question, GIBBERISH.

Twit.

Infinity does not exist when talking of numbers or any thing within the universe.

Nothing in the universe can calculate 0.999999..... and therefore some people just equate it to one. However, even infinity has limits since the concept of infinity does not exist in the universe.

Therefore 0.0...1 is a a number and does not equal zero. I put a one there fore a reason becuase infinity in this regard ends.

Hey chief, you have NO CLUE what you're talking about, so how about you just mosey along. You haven't the slightest grasp on the matter. Trust me.

0.0...1 is gibberish. It's as much a naked woman as it is a number. Sound ridiculous? That's because it is.

.999 repeats INFINITELY. Infinity is not a number: it's a concept. It's the concept of a never-ending "thing", in this case, 9's. By definition, nothing can follow it.

I feel like I'm talking to a child.

Originally posted by: Injury
I failed calculus FFS. Twice.

You don't say.

If infinity is not a number, how can 0.999... (which has infinity 9s and therefore is NOT A REAL NUMBER) equal to one? (Which is a REAL NUMBER?) sounds ridiculous to me!!!

If 0.0...1 is not an accepted number, why is 0.99..?

Its like equating chickens and hands!

Holy cow. You're right, son. You're smarter than all of the PhD holding mathematicians dead or alive.

1. You can't put anything at the end of infinite object. That's like saying "at the end of forever, there's a '1'". No one is calling 'infinity' a number. It simply means that the 0's in 0.000... are never ending, and the 9's in 0.999... are never ending.

2. The value of whatever position you claim '1' to hold in '0.000...1' is already defined. You already stated that '0' repeats forever. '0.000...1' contradicts itself, which is why it's total gibberish. You can't say "0 repeats forever, but at some point there's a '1'". At any point in 'forever', you've stated there's a '0'. The only reason you put a '1' there is because you cannot grasp 'infinity'. Just because you cannot grasp it doesn't mean it's wrong.

3. I can show you two basic proofs and one "advanced" one that illustrates precisely why 0.999... = 1, but I'm certain such an effort would be a waste. If you want to see them, read the Wikipedia article. These are widely accepted (among professional mathematicians). If you wish to challenge any of the three proofs, you must first prove one of the assumptions false. Good luck with that. If you do not understand any one of these three proofs, you are hardly qualified to even be engaging in this discussion or challenging those who do understand them... for the same reasons I don't get into discussions over thermodynamics and quantum theory. It would be preposterous.

I know I'm being rude, but I assure you it's only in response to your incredible arrogance.

Point three, which I bolded, is exactly what I asked for from the doubters in the previous "0.999... = 1" thread; instead of using math to disprove the proofs given, all I got were peoples opinions...

Have you even read the article?

 

[jman19]

Originally posted by: RapidSnail

Originally posted by: jman19

Originally posted by: jbourne77

Originally posted by: The Green Bean

Originally posted by: jbourne77

Originally posted by: The Green Bean

Originally posted by: jbourne77

Originally posted by: The Green Bean
.99999...is not eual to one. Its 1 - 0.000000000......1

Sadly, dumb people will never realize that mere earthlings will NEVER be able to grasp the concept of infinity.

Speaking of dumb people, dumbass, "0.000000000......1" is not even a number. It's no more a number than 1.0.0.03.0.3.dkx.33.Qfuck.03 is a number. It's just an arbitrary arrangement of characters that you've thrown together in a vein attempt to make others look less intelligent than yourself, when in fact, you've proven - quite well, I might add - just the opposite.

The "1" never comes into play. You've already stated there is an infinite number of 0's and, as such, you've already defined 0 for the place value wherever which you think 1 resides. Infinity is forever. You don't just waltz to the end of it and slap a 1 on for good measure.

In short, 0.000... is ALWAYS, without question, ZERO.
0.000...x is ALWAYS, without question, GIBBERISH.

Twit.

Infinity does not exist when talking of numbers or any thing within the universe.

Nothing in the universe can calculate 0.999999..... and therefore some people just equate it to one. However, even infinity has limits since the concept of infinity does not exist in the universe.

Therefore 0.0...1 is a a number and does not equal zero. I put a one there fore a reason becuase infinity in this regard ends.

Hey chief, you have NO CLUE what you're talking about, so how about you just mosey along. You haven't the slightest grasp on the matter. Trust me.

0.0...1 is gibberish. It's as much a naked woman as it is a number. Sound ridiculous? That's because it is.

.999 repeats INFINITELY. Infinity is not a number: it's a concept. It's the concept of a never-ending "thing", in this case, 9's. By definition, nothing can follow it.

I feel like I'm talking to a child.

Originally posted by: Injury
I failed calculus FFS. Twice.

You don't say.

If infinity is not a number, how can 0.999... (which has infinity 9s and therefore is NOT A REAL NUMBER) equal to one? (Which is a REAL NUMBER?) sounds ridiculous to me!!!

If 0.0...1 is not an accepted number, why is 0.99..?

Its like equating chickens and hands!

Holy cow. You're right, son. You're smarter than all of the PhD holding mathematicians dead or alive.

1. You can't put anything at the end of infinite object. That's like saying "at the end of forever, there's a '1'". No one is calling 'infinity' a number. It simply means that the 0's in 0.000... are never ending, and the 9's in 0.999... are never ending.

2. The value of whatever position you claim '1' to hold in '0.000...1' is already defined. You already stated that '0' repeats forever. '0.000...1' contradicts itself, which is why it's total gibberish. You can't say "0 repeats forever, but at some point there's a '1'". At any point in 'forever', you've stated there's a '0'. The only reason you put a '1' there is because you cannot grasp 'infinity'. Just because you cannot grasp it doesn't mean it's wrong.

3. I can show you two basic proofs and one "advanced" one that illustrates precisely why 0.999... = 1, but I'm certain such an effort would be a waste. If you want to see them, read the Wikipedia article. These are widely accepted (among professional mathematicians). If you wish to challenge any of the three proofs, you must first prove one of the assumptions false. Good luck with that. If you do not understand any one of these three proofs, you are hardly qualified to even be engaging in this discussion or challenging those who do understand them... for the same reasons I don't get into discussions over thermodynamics and quantum theory. It would be preposterous.

I know I'm being rude, but I assure you it's only in response to your incredible arrogance.

Point three, which I bolded, is exactly what I asked for from the doubters in the previous "0.999... = 1" thread; instead of using math to disprove the proofs given, all I got were peoples opinions...

Have you even read the article?

Yes, I did. What does that have to do with asking for proof rather than opinions?

 

[Born2bwire]

Originally posted by: Pastore
How can a plane take off with no lift? i.e. the plane is stationary.

You have to realize that the conveyor belt does not keep the plane stationary. That is the point. Yes the conveyor belt will apply a reverse force against the force of the engines. But realize that this force is very small, in addition, even if we made the force to be dependent on the speed of the conveyor belt, this force gradually ramps up as the speed of the belt increases. So the correct statement of the problem will restrict the belt from ramping up to a high enough speed, which would be a rather insane speed, nigh ludicrous, before the plane achieves a fast enough forward velocity to take off. For example, we say that the speed of the belt is equal to the speed of the plane relative to the ground. This means that the speed of the wheels is twice what it would normally be if the plane was taking off from a stationary surface.

A lot of the confusion that I see generally lies with poor statements of the problem that contradict what the problem is or should be asking. For example, I think that the one on ATOT before stated that the belt moved in such a way that the plane remains stationary. Well this isn't a logical question to ask because we are forcing an obvious no win situation. Others say that the belt is the same speed of the wheels relative to the belt or the same speed as the plane relative to the belt. These are incorrect because the speed of the wheels is dependent upon both the forward motion of the plane and the speed of the belt. In the second case, we again implicitly make the speed of the belt dependent on itself. What this creates is a paradox in that as soon as any motion occurs with the plane (which we can assume since we start at rest, the only initial force that needs to be overcome is static friction and for any plane to work the jets have to overcome this), the speed of the belt ramps up to infinity. The only way that we can satisfy the relationship that V_belt = V_wheels = V_belt+V_plane is when the plane has no forward motion. But we see that this requirement has nothing to do with the physics, this requirement is a consequence of a poor statement of the problem. So the only way for this to work is if we have some kind of lag in the control system of the belt, but that means that the belt will lag behind the plane's motion and then we can still argue that the plane can take off.

 

[Stuxnet]

Originally posted by: jman19
Point three, which I bolded, is exactly what I asked for from the doubters in the previous "0.999... = 1" thread; instead of using math to disprove the proofs given, all I got were peoples opinions...

Linkorama

 

[Stuxnet]

Regarding the plane: If the wheels were the plane's SOURCE OF POWER, then it would not be able to take off. The conveyor belt does not negate the thrust from the jet engines, however.

In reality, the wheels only exist so the plane's fuselage isn't destroyed by skidding along the ground on takeoffs and landings. In a car, however, the wheels are where the transfer of power are.

 

[jman19]

Originally posted by: jbourne77

Originally posted by: jman19
Point three, which I bolded, is exactly what I asked for from the doubters in the previous "0.999... = 1" thread; instead of using math to disprove the proofs given, all I got were peoples opinions...

Linkorama

I'm confused, why are you linking me to the wiki page? I've already read it.

 

[Pastore]

Originally posted by: Born2bwire

Originally posted by: Pastore
How can a plane take off with no lift? i.e. the plane is stationary.

You have to realize that the conveyor belt does not keep the plane stationary. That is the point. Yes the conveyor belt will apply a reverse force against the force of the engines. But realize that this force is very small, in addition, even if we made the force to be dependent on the speed of the conveyor belt, this force gradually ramps up as the speed of the belt increases. So the correct statement of the problem will restrict the belt from ramping up to a high enough speed, which would be a rather insane speed, nigh ludicrous, before the plane achieves a fast enough forward velocity to take off. For example, we say that the speed of the belt is equal to the speed of the plane relative to the ground. This means that the speed of the wheels is twice what it would normally be if the plane was taking off from a stationary surface.

A lot of the confusion that I see generally lies with poor statements of the problem that contradict what the problem is or should be asking. For example, I think that the one on ATOT before stated that the belt moved in such a way that the plane remains stationary. Well this isn't a logical question to ask because we are forcing an obvious no win situation. Others say that the belt is the same speed of the wheels relative to the belt or the same speed as the plane relative to the belt. These are incorrect because the speed of the wheels is dependent upon both the forward motion of the plane and the speed of the belt. In the second case, we again implicitly make the speed of the belt dependent on itself. What this creates is a paradox in that as soon as any motion occurs with the plane (which we can assume since we start at rest, the only initial force that needs to be overcome is static friction and for any plane to work the jets have to overcome this), the speed of the belt ramps up to infinity. The only way that we can satisfy the relationship that V_belt = V_wheels = V_belt+V_plane is when the plane has no forward motion. But we see that this requirement has nothing to do with the physics, this requirement is a consequence of a poor statement of the problem. So the only way for this to work is if we have some kind of lag in the control system of the belt, but that means that the belt will lag behind the plane's motion and then we can still argue that the plane can take off.

From the Wikipedia article...

"A plane is standing on a runway that can move (some sort of conveyer belt). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

This does lead a person to believe the conveyor would keep the plane stationary. Obviously if the conveyor does not keep the plane stationary, the whole thing is moot.

 

[Stuxnet]

Originally posted by: jman19

Originally posted by: jbourne77

Originally posted by: jman19
Point three, which I bolded, is exactly what I asked for from the doubters in the previous "0.999... = 1" thread; instead of using math to disprove the proofs given, all I got were peoples opinions...

Linkorama

I'm confused, why are you linking me to the wiki page? I've already read it.

Sorry... thought you were requesting it. My bad.

 

[bigredguy]

see sig

 

[Born2bwire]

Originally posted by: Pastore

Originally posted by: Born2bwire

Originally posted by: Pastore
How can a plane take off with no lift? i.e. the plane is stationary.

You have to realize that the conveyor belt does not keep the plane stationary. That is the point. Yes the conveyor belt will apply a reverse force against the force of the engines. But realize that this force is very small, in addition, even if we made the force to be dependent on the speed of the conveyor belt, this force gradually ramps up as the speed of the belt increases. So the correct statement of the problem will restrict the belt from ramping up to a high enough speed, which would be a rather insane speed, nigh ludicrous, before the plane achieves a fast enough forward velocity to take off. For example, we say that the speed of the belt is equal to the speed of the plane relative to the ground. This means that the speed of the wheels is twice what it would normally be if the plane was taking off from a stationary surface.

A lot of the confusion that I see generally lies with poor statements of the problem that contradict what the problem is or should be asking. For example, I think that the one on ATOT before stated that the belt moved in such a way that the plane remains stationary. Well this isn't a logical question to ask because we are forcing an obvious no win situation. Others say that the belt is the same speed of the wheels relative to the belt or the same speed as the plane relative to the belt. These are incorrect because the speed of the wheels is dependent upon both the forward motion of the plane and the speed of the belt. In the second case, we again implicitly make the speed of the belt dependent on itself. What this creates is a paradox in that as soon as any motion occurs with the plane (which we can assume since we start at rest, the only initial force that needs to be overcome is static friction and for any plane to work the jets have to overcome this), the speed of the belt ramps up to infinity. The only way that we can satisfy the relationship that V_belt = V_wheels = V_belt+V_plane is when the plane has no forward motion. But we see that this requirement has nothing to do with the physics, this requirement is a consequence of a poor statement of the problem. So the only way for this to work is if we have some kind of lag in the control system of the belt, but that means that the belt will lag behind the plane's motion and then we can still argue that the plane can take off.

From the Wikipedia article...

"A plane is standing on a runway that can move (some sort of conveyer belt). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

This does lead a person to believe the conveyor would keep the plane stationary. Obviously if the conveyor does not keep the plane stationary, the whole thing is moot.

Nothing in that statement implies that the conveyor belt is keeping the plane stationary. It states that the conveyor belt is moving at the same speed of the plane, but in the opposite direction. You need to remember that the wheels on a plane are free moving, they're nothing more than caster wheels.

 

[Stuxnet]

The conveyor belt could be traveling at eleventy billion miles per hour. Friction and wheel durability aside, the plane would still require the same amount of thrust over the same distance to take off. Like Born2bwire said, the wheels are free moving. They're not the source of power, so their motion is irrelevant to the plane.

 

[The Green Bean]

Originally posted by: RapidSnail
So many people lose sight of the fact that .9bar is an infinitely repeating number. It never ends. When you say .9...1 you are really saying .9 repeating to x amount of places with a one on the end. That number is not equal to one, and nobody ever said it did. You have to realize that infinity is not an ever expanding number. It is just there.

Most people imagine an infinite series as a number constantly racing towards infinity, as if it is a train constantly moving foward at an extremely rapid pace. However, infinity is already a point in space. We just happen to be moving "closer" along the number line to it as we expand our view of it. Think of the largest number you can. What you just thought of was not a "new" number. You did not just "expand" the number line by "inventing" a number larger than your previous scope, what you did do was expand your view of the number line to include a number you previously did not have knowledge of bringing you that much "closer" to infinity.

Understand the .9bar is a set number, not one approaching infinity, but one already at infinity. Knowing that, we see through all sorts of proofs that it is equal to one. For a simple example, give me a number inbetween .9bar and one. When you find that number, let me know. And I'll give you a hint, it's not .9...y, because at the point you come to an ending digit, you have stopped the infinite series and reduced it to a finite number, .9... x 10^-x + y x 10^-x+1.

In this post, "bar" is equivalent to "infinitely repeating," and "..." is equivalent to "repeating." Both have the same meaning in mathematics, but I am redefining them for this post so I don't have to write "repeating" whenever I wish to express a number not infinitely repeating in an equation. Also, italicized "x" means "multiplied by" or "times," and regular "x" is an independent variable.

Edit - Fixed equation.

From what I understand, a trillion is not any closer to infinity than 1 is.

 

[The Green Bean]

Originally posted by: jbourne77
Regarding the plane: If the wheels were the plane's SOURCE OF POWER, then it would not be able to take off. The conveyor belt does not negate the thrust from the jet engines, however.

In reality, the wheels only exist so the plane's fuselage isn't destroyed by skidding along the ground on takeoffs and landings. In a car, however, the wheels are where the transfer of power are.

Why havent they made planes that can take off when stationary? Doesnt make sense to me.

 

[timosyy]

This is awesome- should be a sticky.

We have the plane taking off & .999 = 1 in the SAME thread!

epic.

 

[iamaelephant]

Originally posted by: timosyy
This is awesome- should be a sticky.

We have the plane taking off & .999 = 1 in the SAME thread!

epic.

This is a big day for ATOT.

 

[Suspicious-Teach8788]

Originally posted by: The Green Bean

Originally posted by: RapidSnail
So many people lose sight of the fact that .9bar is an infinitely repeating number. It never ends. When you say .9...1 you are really saying .9 repeating to x amount of places with a one on the end. That number is not equal to one, and nobody ever said it did. You have to realize that infinity is not an ever expanding number. It is just there.

Most people imagine an infinite series as a number constantly racing towards infinity, as if it is a train constantly moving foward at an extremely rapid pace. However, infinity is already a point in space. We just happen to be moving "closer" along the number line to it as we expand our view of it. Think of the largest number you can. What you just thought of was not a "new" number. You did not just "expand" the number line by "inventing" a number larger than your previous scope, what you did do was expand your view of the number line to include a number you previously did not have knowledge of bringing you that much "closer" to infinity.

Understand the .9bar is a set number, not one approaching infinity, but one already at infinity. Knowing that, we see through all sorts of proofs that it is equal to one. For a simple example, give me a number inbetween .9bar and one. When you find that number, let me know. And I'll give you a hint, it's not .9...y, because at the point you come to an ending digit, you have stopped the infinite series and reduced it to a finite number, .9... x 10^-x + y x 10^-x+1.

In this post, "bar" is equivalent to "infinitely repeating," and "..." is equivalent to "repeating." Both have the same meaning in mathematics, but I am redefining them for this post so I don't have to write "repeating" whenever I wish to express a number not infinitely repeating in an equation. Also, italicized "x" means "multiplied by" or "times," and regular "x" is an independent variable.

Edit - Fixed equation.

From what I understand, a trillion is not any closer to infinity than 1 is.

You are correct and this is what many people don't understand.

When asked where the middle of the number line is, most people point to ZERO (0), but that is obviously false.

Originally posted by: iamaelephant

Originally posted by: timosyy
This is awesome- should be a sticky.

We have the plane taking off & .999 = 1 in the SAME thread!

epic.

This is a big day for ATOT.

Damn.. So we can have like 5000 posts merged into 1 thread =]. YAY! :beer:

 

[silverpig]

Originally posted by: DLeRium

When asked where the middle of the number line is, most people point to ZERO (0), but that is obviously false.

...but it's as good an answer as any

 

[Stuxnet]

Originally posted by: The Green Bean

Originally posted by: jbourne77
Regarding the plane: If the wheels were the plane's SOURCE OF POWER, then it would not be able to take off. The conveyor belt does not negate the thrust from the jet engines, however.

In reality, the wheels only exist so the plane's fuselage isn't destroyed by skidding along the ground on takeoffs and landings. In a car, however, the wheels are where the transfer of power are.

Why havent they made planes that can take off when stationary? Doesnt make sense to me.

The obvious answer is because the conventional needs a runway to pick up enough speed to generate the proper amount of lift.

 

[RapidSnail]

Originally posted by: The Green Bean

Originally posted by: RapidSnail
So many people lose sight of the fact that .9bar is an infinitely repeating number. It never ends. When you say .9...1 you are really saying .9 repeating to x amount of places with a one on the end. That number is not equal to one, and nobody ever said it did. You have to realize that infinity is not an ever expanding number. It is just there.

Most people imagine an infinite series as a number constantly racing towards infinity, as if it is a train constantly moving foward at an extremely rapid pace. However, infinity is already a point in space. We just happen to be moving "closer" along the number line to it as we expand our view of it. Think of the largest number you can. What you just thought of was not a "new" number. You did not just "expand" the number line by "inventing" a number larger than your previous scope, what you did do was expand your view of the number line to include a number you previously did not have knowledge of bringing you that much "closer" to infinity.

Understand the .9bar is a set number, not one approaching infinity, but one already at infinity. Knowing that, we see through all sorts of proofs that it is equal to one. For a simple example, give me a number in between .9bar and one. When you find that number, let me know. And I'll give you a hint, it's not .9...y, because at the point you come to an ending digit, you have stopped the infinite series and reduced it to a finite number, .9... x 10^-x + y x 10^-x+1.

In this post, "bar" is equivalent to "infinitely repeating," and "..." is equivalent to "repeating." Both have the same meaning in mathematics, but I am redefining them for this post so I don't have to write "repeating" whenever I wish to express a number not infinitely repeating in an equation. Also, italicized "x" means "multiplied by" or "times," and regular "x" is an independent variable.

Edit - Fixed equation.

From what I understand, a trillion is not any closer to infinity than 1 is.

Did you see the parentheses around the word? I was merely trying to prove a point about infinity. I was assuming you all would be able to discern that.

 

[ultimatebob]

GEEK FIGHT! Break out the plastic Light Sabers, we're having a throw down!

 

[Stuxnet]

Originally posted by: RapidSnail
I was assuming you all would be able to discern that.

You've apparently not read his other posts .

 

[RapidSnail]

Originally posted by: jbourne77

Originally posted by: RapidSnail
I was assuming you all would be able to discern that.

You've apparently not read his other posts .

Maybe I shouldn't .

 

[The Green Bean]

Why isnt 0.22222.... = 1? Since there is not end to the twos, you might as well equate it to 1.

 

[TheoPetro]

Originally posted by: The Green Bean
Why isnt 0.22222.... = 1? Since there is not end to the twos, you might as well equate it to 1.

I can put a number, 0.2333... between .222... and 1. Show me a number between .999... and 1.

 

[fitzov]

Originally posted by: TheoPetro

Originally posted by: The Green Bean
Why isnt 0.22222.... = 1? Since there is not end to the twos, you might as well equate it to 1.

I can put a number, 0.2333... between .222... and 1. Show me a number between .999... and 1.

In the proof it would be denoted by an infinitesimal ("1/10^H" I believe), as in

a(sub)H is < or = 1 which is < or = a(sub)H + 1/10^H