The plane takes off, 0.999... = 1, but what about...

[SilthDraeth]

Say you have x = .9999999999999999....
multiply both sides by 10, and subtract the original from it.

10x = 9.99999999999999999...
-x = 0.99999999999999999...
9x = 9
x=1

Lets try this again. But lets just use 5 (9s)
x = .99999... (multiply both sides by 10)
10x= 9.9999... (correct so far) 9.9999/10=x (x=.99999)
Then you say subtract the original from it.
(10x)-x does equal 9x This is where your logic becomes flawed.
(10x=9.9999) - (x=.99999)= 8.99991 which doesn't equal 9
9x= (9)x(.99999)= 8.99991

But X does not in fact equal 1. 9/8.99991 x actually equals .99999

 

[JohnCU]

Originally posted by: 91TTZ

Originally posted by: JohnCU
If you have 2 liquids (you don't know what they are), 1 mL of each and you add them together, can you be 100% sure that the resulting solution is 2 mL?

No.

Mix ethanol and water. You won't have 2 ml. Water and ethanol are miscable, and the alcohol absorbs water.

:thumbsup:

 

[SoulAssassin]

mythbusters should do the plane on a runway thing

 

[her209]

Whoa, its like WinZip, but in real life! :Q

 

[msparish]

Originally posted by: SilthDraeth
Say you have x = .9999999999999999....
multiply both sides by 10, and subtract the original from it.

10x = 9.99999999999999999...
-x = 0.99999999999999999...
9x = 9
x=1

Lets try this again. But lets just use 5 (9s)
x = .99999... (multiply both sides by 10)
10x= 9.9999... (correct so far) 9.9999/10=x (x=.99999)
Then you say subtract the original from it.
(10x)-x does equal 9x This is where your logic becomes flawed.
(10x=9.9999) - (x=.99999)= 8.99991 which doesn't equal 9
9x= (9)x(.99999)= 8.99991

But X does not in fact equal 1. 9/8.99991 x actually equals .99999

You have a misunderstanding of the concept of infinity.

 

[GasX]

if the two liquids are bleach and ammonia the resulting mixture is about 0 mL

 

[Brainonska511]

Originally posted by: msparish

Originally posted by: SilthDraeth
Say you have x = .9999999999999999....
multiply both sides by 10, and subtract the original from it.

10x = 9.99999999999999999...
-x = 0.99999999999999999...
9x = 9
x=1

Lets try this again. But lets just use 5 (9s)
x = .99999... (multiply both sides by 10)
10x= 9.9999... (correct so far) 9.9999/10=x (x=.99999)
Then you say subtract the original from it.
(10x)-x does equal 9x This is where your logic becomes flawed.
(10x=9.9999) - (x=.99999)= 8.99991 which doesn't equal 9
9x= (9)x(.99999)= 8.99991

But X does not in fact equal 1. 9/8.99991 x actually equals .99999

You have a misunderstanding of the concept of infinity.

Infinite levels of infinity.... That is the correct way of doing it. It's how you turn repeating decimals into fraction.

 

[randay]

Originally posted by: SoulAssassin
mythbusters should do the plane on a runway thing

well, theres your problem!

 

[Brainonska511]

Originally posted by: Mwilding
if the two liquids are bleach and ammonia the resulting mixture is about 0 mL

He said later in the thread that they don't react. The example given later was Ethanol and Water. They are miscible, so the final volume is less than 2mL.

 

[cyclohexane]

no, mixing sulfuric acid and water will result in so much heat release that you'll lose a lot of volume.

 

[BrownTown]

.99999 DOES EQUAL 1 (this is not up for debate, if you don't understand why this is true thats your own fault, but this is a fact in mathematics)

Mixing ethanol and water results in a considerbly smaller volume since they hydrogen bond tightly and become more dense, there are hundreds of other examples, but ethanol + water is most famous.

Whats this plane taking off thing, never heard that b4?

 

[FoBoT]

2 ml is hardly bulk anything :roll:

 

[Kyteland]

Originally posted by: BrownTown
Whats this plane taking off thing, never heard that b4?

http://www.straightdope.com/columns/060203.html

 

[jagec]

Originally posted by: BrownTown
.99999 DOES EQUAL 1 (this is not up for debate, if you don't understand why this is true thats your own fault, but this is a fact in mathematics)

Mixing ethanol and water results in a considerbly smaller volume since they hydrogen bond tightly and become more dense, there are hundreds of other examples, but ethanol + water is most famous.

Whats this plane taking off thing, never heard that b4?

You've got a plane on a conveyor belt. When the plane moves forwards, the conveyor matches its speed in reverse. Can the plane take off?

The debate mostly centers on the definition of "matching the plane's speed in reverse."

There is a way to stop the plane from taking off if we use ideal physics (ie everything is indestructible) and a certain reading of the control system, but in all other cases the plane takes off.

 

[Syringer]

Originally posted by: BrownTown
.99999 DOES EQUAL 1 (this is not up for debate, if you don't understand why this is true thats your own fault, but this is a fact in mathematics)

No it doesn't

Mixing ethanol and water results in a considerbly smaller volume since they hydrogen bond tightly and become more dense, there are hundreds of other examples, but ethanol + water is most famous.

Whats this plane taking off thing, never heard that b4?

If a plane is on a conveyor belt, will it take off?

 

[Rayden]

Water and alcohol mixed together will take up less space than the two seperate.

 

[DrPizza]

Ummm, I'm going to have to disagree with the "mass is conserved" people as well. If a chemical reaction takes place, mass is lost to energy.

 

[everman]

It depends on if there's a chemical reaction, also if the plane takes off and whether or not .999 = 5.

 

[DrPizza]

.9999...=0!

 

[BrownTown]

DrPizza, attempting to point out the fact that mass is lost in a chemical reaction is really pushing it. For all practical purposes mass is considered to be conserved. I guarentee you if I took a chemical engineering class and said i couldn't solve a problem using conservation of mass becasue the chemical reaction would lose mass the professor would fail me. (and probably call me an idiot too)

 

[SilthDraeth]

Originally posted by: jagec

Originally posted by: BrownTown
.99999 DOES EQUAL 1 (this is not up for debate, if you don't understand why this is true thats your own fault, but this is a fact in mathematics)

Mixing ethanol and water results in a considerbly smaller volume since they hydrogen bond tightly and become more dense, there are hundreds of other examples, but ethanol + water is most famous.

Whats this plane taking off thing, never heard that b4?

You've got a plane on a conveyor belt. When the plane moves forwards, the conveyor matches its speed in reverse. Can the plane take off?

The debate mostly centers on the definition of "matching the plane's speed in reverse."

There is a way to stop the plane from taking off if we use ideal physics (ie everything is indestructible) and a certain reading of the control system, but in all other cases the plane takes off.

About to go read the link. But is the plan actually "moving forward", or staying in place.

Not that it matters.

Editing again. Of course my initial question was dumb, until I thought about it.

 

[BrownTown]

The plane is moving forward becasue the motion of the wheels and the forward motion are not related assuming that the parts are well oiled and such. In reality there would be a little additional drag due to the spinning wheels, but it would be neglidgible unless the conveyor belt was going reallf really fast.

 

[DrPizza]

Originally posted by: BrownTown
DrPizza, attempting to point out the fact that mass is lost in a chemical reaction is really pushing it. For all practical purposes mass is considered to be conserved. I guarentee you if I took a chemical engineering class and said i couldn't solve a problem using conservation of mass becasue the chemical reaction would lose mass the professor would fail me. (and probably call me an idiot too)

Is mass conserved in a chemical reaction? No. Is the loss in mass negligible? Yes. The answer to the second question does not change the answer to the first question.

 

[Acanthus]

Originally posted by: FoBoT
2 ml is hardly bulk anything :roll:

bulk dark matter!

 

[BigPoppa]

Easy to baby step someone through this, mix a cup of water and a cup of sugar. Wow its not 2 cups of volume? Proceed to liquids.

Ponder: Can gases be "miscible" in each other or does it not work at that point? Trying to baby step my way through that one, liquid + gas, but not giving me the visual I want. Haven't ever covered like that in any of my chem courses.