0.9999 . . . = 1? It sure seems so.

What always messed me up is thinking about how you could divide the distance between two objects in half and never arrive at zero, ergo they would never touch.
:confused:

Math and science were never my strong suits.
 
Blais said:
What always messed me up is thinking about how you could divide the distance between two objects in half and never arrive at zero, ergo they would never touch.
:confused:

Math and science were never my strong suits.
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Zeno's paradox. The good news is it has been proven incorrect - you can walk across the room and touch the wall after all.
 
UffDa said:
I reached my level of incompetence in math at..............

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UffDa said:
It's not a difficult concept. Let's say that 1 gallon of gas costs $3.29 9/10. Since there is no 9/10 cent coin, you have to either buy a little more or a little less, but you can not buy exactly 1 gallon.
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You should have stopped at pie. Of course you can buy exactly one gallon of gasoline... It is the bill that will be rounded not the quantity of gas. Btw, grocery stores do the same thing - and they always round in their favor.
 
This is nothing new Powernoodle, didn't you take Algebra II? Fortunately many states include Algebra II as a graduating prerequisite but the National Standards don't. Your son is fortunate to have a teacher that requires him to think.
 
sheepdog229 said:
You should have stopped at pie. Of course you can buy exactly one gallon of gasoline... It is the bill that will be rounded not the quantity of gas. Btw, grocery stores do the same thing - and they always round in their favor.
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sheepdog229, you are missing the point. You can not buy 1 gallon of gas for the listed price. The price will be rounded UP to the next penny. Obviously, you can buy exactly 1 gallon, but it will cost you 1/10¢ more then the listed price.

So, what's the big deal with the 9/10¢? How about $1.7 billion a year?
 
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OldPhysics said:
You should try theoretical physics + laser physics + modern optics + solid state physics + quantum mechanics. Add a little dash of national security ... even my mother won't talk to me.

If she were still alive.
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Science sure has gotten colorful lately.

startinside.jpg
 
it might be better to think about it abstractly, you have 1 cup of water and you pour equal amounts into 3 cups, each cup has 1/3, you know that 1/3 = .333333333...etc but if you put all the cups together you get 1
 
SilentLynx said:
it might be better to think about it abstractly, you have 1 cup of water and you pour equal amounts into 3 cups, each cup has 1/3, you know that 1/3 = .333333333...etc but if you put all the cups together you get 1
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That appears to work when you are being practical. However when you think about it deeper, technically you cannot separate anything into 3 equal parts. You can get close but not exact.

You would end up with .33, .33, .34 (doesn't matter how many decimal places you go they will only be equal when you reach infinity - good luck getting there)

Edit: I shouldn't have said you can't divide "anything" into 3 = parts. Obviously you can take a 3" string and divide it into 3 1" peices. Let's just stick to water for the example.
 
Root cause of the problem, 1/3 != .333333333333... go on as long as you want. Its an approximation. Also, infinite doesn't exist. The idea does, the actual quantity doesn't.
 
sheepdog229 said:
That appears to work when you are being practical. However when you think about it deeper, technically you cannot separate anything into 3 equal parts. You can get close but not exact.

You would end up with .33, .33, .34 (doesn't matter how many decimal places you go they will only be equal when you reach infinity - good luck getting there)

Edit: I shouldn't have said you can't divide "anything" into 3 = parts. Obviously you can take a 3" string and divide it into 3 1" peices. Let's just stick to water for the example.
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Water seems to be a more divisible substance than a string with an inconstant number of particles for equal given lengths. You can divide a glass of water in 3 equal parts if you have an amount with a total # of molecules that is divisible by 3 and a measuring system that can count the individual molecules. You would also have to eliminate all evaporation or keep it at a constant between the 3 glasses.
 
bushidomosquito said:
Water seems to be a more divisible substance than a string with an inconstant number of particles for equal given lengths. You can divide a glass of water in 3 equal parts if you have an amount with a total # of molecules that is divisible by 3 and a measuring system that can count the individual molecules. You would also have to eliminate all evaporation or keep it at a constant between the 3 glasses.
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Those are big "ifs" but I agree with the argument.

If I bake an apple pie can we divide it into 3 = parts? I guess if we are lucky enough or smart enough to have a total # of molecules that are divisable by 3.

In any event, .9bar does not = 1, it merely approximates 1.
 
Hawk_7575 said:
Root cause of the problem, 1/3 != .333333333333... go on as long as you want. Its an approximation. Also, infinite doesn't exist. The idea does, the actual quantity doesn't.
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Without infinity most grad students and graduates in science, engineering and math would be out of school/jobs. Converging limits, integration and many equations used for those fields that are then turned into practical items/work/designs may require these theories.

sheepdog229 said:
That appears to work when you are being practical. However when you think about it deeper, technically you cannot separate anything into 3 equal parts. You can get close but not exact.

You would end up with .33, .33, .34 (doesn't matter how many decimal places you go they will only be equal when you reach infinity - good luck getting there)

Edit: I shouldn't have said you can't divide "anything" into 3 = parts. Obviously you can take a 3" string and divide it intopiecespeices. Let's just stick to water for the example.
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1 yard = 3 feet
1 foot = 1/3 of a yard
So we can divide a yard into 3 parts and add them back together as many times as we like and always end up with a full yard each time.

divide the yard by 3 and add the 3 feet back together again one million times and we still end up with a yard.
We never lose the 0.0000000...01

1/3 = 0.333333333333333333....
1/3 != 0.333333333333333...3 (approximation)
1/3 != 0.333333333333333...4 (approximation)

From calculus I or II ( I can't remember) infinity is required. Isn't life fun?
 
If you people have this much time to think about this mind bending stuff..................you need more knives to play with!!!
 
gga357 said:
Without infinity most grad students and graduates in science, engineering and math would be out of school/jobs. Converging limits, integration and many equations used for those fields that are then turned into practical items/work/designs may require these theories.
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True, but have you ever seen a bridge that is infinity feet long? Or a building infinity feet tall? They're called imaginary/complex numbers for a reason. They don't actually exist, only the idea does.
 
Hawk_7575 said:
True, but have you ever seen a bridge that is infinity feet long? Or a building infinity feet tall? They're called imaginary/complex numbers for a reason. They don't actually exist, only the idea does.
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Guess I never needed to see infinity to use it.

I do know what zero is and one of my favorite things to do is divide by zero. :cool: ;)
 
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