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To Maelwys
Quote: " 1.5000... = 1.4999... "
A.R.B
1.5000... - 1.4999... = 0.0001 this is an Infinite Calculation! and can be proved the same Difference exists! no matter how many decimal places you want to try!
Example A = Infinite ( 1.50 ) B = Infinite ( 1.49 ) A - B = 0.001...
We're already having this argument and don't need to start it all over again, I was just explaining what Sekky meant by his statement.
Now if you could respond to my other question to you a few posts up, that'd be great thanks.
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To Maelwys
A.R.B
remind me! it would help if you only gave one reply! but I may have to go for now!
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Post # 589, which was my only reply at the time.
Instead of just countering points, I'll try posting one of my own for Anthony to counter.
If 0.999... is 0.000...1 difference from 1, where 0.000...1 has an infinite amount of 0s, followed by(?) a 1, then what is half of the value of 0.000...1? For any two numbers that are not equal, we should be able to find the average of those two numbers, being equal to half the difference between them. So the average of 0.999... and 1 should be equal to 0.999... + (0.000...1 / 2), so I'm wondering how you believe we'd be able to do that math, and what the answer should be?
Also, you conveniently answered only half of post # 587, pointing out that my initial translation of it was incorrect, but then never actually answering my correct translation of it, by explaining how 0.555.... = 0.5, when there's a 0.0555... difference between them.
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To Sekky
A.R.B
when the apple falls on your head! you may wake up!! but untill then! take notes from someone who knows more then you!
Then take notes from me, I'm a professional, you're not, and I would rarely ever say this to an aspiring mathematician, but learn your place. You aren't as good as me, and you're years from ever reaching that level, and if you don't shut up and start accepting basic facts about field theory, you will never reach that level.
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To Sekky
Quote: " start accepting basic facts about field theory "
A.R.B
I am more than sure!! the only field theory you really know about! is being in a field! with field mice!..
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Hey guys, can we please get away from the insults and back to the mathmatical discussion?
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To Maelwys
Quote:"
If 0.999... is 0.000...1 difference from 1, where 0.000...1 has an infinite amount of 0s, followed by(?) a 1, then what is half of the value of 0.000...1?
A.R.B
0.1 / 2 = 0.05 and another example 0.01 / 2 = 0.005 Infinite example = ( 0.001...) / 2 = ( 0.0005...)
For any two numbers that are not equal, we should be able to find the average of those two numbers, being equal to half the difference between them. So the average of 0.999... and 1 should be equal to 0.999... + (0.000...1 / 2), so I'm wondering how you believe we'd be able
to do that math, and what the answer should be?
A.R.B
0.9 / 2 = 0.45 and another example 0.99 / 2 = 0.495 Infinite example = ( 0.999...) / 2 = ( 0.4995...)
So ( 0.9 ) = ( 0.45 ) + ( 0.05 ) = 0.50
So ( 0.99 ) = ( 0.495 ) + ( 0.005 ) = 0.50
and Infinite ( 0.999...) = ( 0.4995...) + ( 0.0005...) = 0.50
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Quote: "
Also, you conveniently answered only half of post # 587, pointing out that my initial translation of it was incorrect, but then never actually answering my correct translation of it, by explaining how 0.555.... = 0.5, when there's a 0.0555... difference between them.
A.R.B
If your 0.555... is an Infinite Recurring ( 0.5 ) then as we all know the Value is Infinitely Repeating Itself! so the Value will always be the same! length makes no difference!
Infinite Recurring ( 0.5 ) = 0.5 because! ( 0.5 ) will always = 0.5
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To Maelwys
Quote:"
If 0.999... is 0.000...1 difference from 1, where 0.000...1 has an infinite amount of 0s, followed by(?) a 1, then what is half of the value of 0.000...1?
A.R.B
0.1 / 2 = 0.05 and another example 0.01 / 2 = 0.005 Infinite example = ( 0.001...) / 2 = ( 0.0005...)
So if half of 0.000...1 = 0.000...5, then what is 0.000...1 * 5? When there's an infinite number of 0s before the 1, how do you add one zero to show that the 5 is actually smaller than the 1, and not bigger than it?
For any two numbers that are not equal, we should be able to find the average of those two numbers, being equal to half the difference between them. So the average of 0.999... and 1 should be equal to 0.999... + (0.000...1 / 2), so I'm wondering how you believe we'd be able
to do that math, and what the answer should be?A.R.B
0.9 / 2 = 0.45 and another example 0.99 / 2 = 0.495 Infinite example = ( 0.999...) / 2 = ( 0.4995...)
So ( 0.9 ) = ( 0.45 ) + ( 0.05 ) = 0.50
So ( 0.99 ) = ( 0.495 ) + ( 0.005 ) = 0.50
and Infinite ( 0.999...) = ( 0.4995...) + ( 0.0005...) = 0.50
I'm not sure what you're trying to say here... I asked for the average of 0.999... and 1.000..., and you gave me a number that's smaller than both of them, so obviously not the average.
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Quote: "
Also, you conveniently answered only half of post # 587, pointing out that my initial translation of it was incorrect, but then never actually answering my correct translation of it, by explaining how 0.555.... = 0.5, when there's a 0.0555... difference between them.
A.R.B
If your 0.555... is an Infinite Recurring ( 0.5 ) then as we all know the Value is Infinitely Repeating Itself! so the Value will always be the same! length makes no difference!
Infinite Recurring ( 0.5 ) = 0.5 because! ( 0.5 ) will always = 0.5
0.555... = 0.5? But I know that 0.555... is the same as 5/9, and 0.5 is the same as 1/2, so there's a difference between them of 1/18, obviously not equal. Or, if you want to avoid fractions, I know that 0.5 < 0.54321 < 0.555..., so if there's a number between the other two numbers, how are they equal?
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To Maelwys
Quote:"
So if half of 0.000...1 = 0.000...5, then what is 0.000...1 * 5? When there's an infinite number of 0s before the 1, how do you add one zero to show that the 5 is actually smaller than the 1, and not bigger than it? "
A.R.B
Why are you trying to Calculate x 5 what has this to do with what you asked!
0.000...1 = 0.000...5, then what is 0.000...1 * 5?
0.1 / 2 = 0.05 so 0.05 x 2 will always be equal to 0.1 again!
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To Maelwys
Quote:"
0.555... = 0.5? But I know that 0.555... is the same as 5/9, and 0.5 is the same as 1/2, so there's a difference between them of 1/18, obviously not equal. Or, if you want to avoid fractions, I know that 0.5 < 0.54321 < 0.555..., so if there's a number between the other two numbers, how are they equal? "
A.R.B
This Math has nothing to do with Infinite Recurring Numbers!
Last edited by Anthony.R.Brown (2007-03-12 03:36:52)
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To Maelwys
Can you just put one clear Question forward at a time! and make is clear! not multiple replys!
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Why are you trying to Calculate x 5 what has this to do with what you asked!
I'm trying to understand the nature of the number 0.000...1 that you've proposed. What is 0.000...1 * 5?
Last edited by Maelwys (2007-03-12 03:45:07)
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To Maelwys
Quote:
" I'm trying to compare two numbers. What is 0.000...1 * 5? "
A.R.B
0.000...1 * 5 " If this is 0.0001 x 5 then = 0.0005 If this is 0.0000001 x 5 then = 0.0000005
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To Maelwys
Quote:
" I'm trying to compare two numbers. What is 0.000...1 * 5? "
A.R.B
0.000...1 * 5 " If this is 0.0001 x 5 then = 0.0005 If this is 0.0000001 x 5 then = 0.0000005
But its not 0.0001 or 0.00000001, it's 0.000...1 with an infinite number of 0s. The ... doesn't refer to an unknown number of digits, it refers to an infinite number of digits. So what is it then?
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To Maelwys
Quote:
"But its not 0.0001 or 0.00000001, it's 0.000...1 with an infinite number of 0s. The ... doesn't refer to an unknown number of digits, it refers to an infinite number of digits. So what is it then?"
A.R.B
Infinite Recurring ( 0.1 ) x 5 = Infinite Recurring ( 0.1 ) Because the Calculation Infinitely Repeats Itself!!
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To Maelwys
Quote:
"But its not 0.0001 or 0.00000001, it's 0.000...1 with an infinite number of 0s. The ... doesn't refer to an unknown number of digits, it refers to an infinite number of digits. So what is it then?"
A.R.B
Infinite Recurring ( 0.1 ) x 5 = Infinite Recurring ( 0.1 ) Because the Calculation Infinitely Repeats Itself!!
What do you mean "the calculation infinitely repeats itself"? Why can't I multiple the number 0.000...1? You told me that 0.000...1 / 2 = 0.000...5 up above, so if I can divide it, why can't I multiply it? Also, when writing it down, please write it as 0.000...1, not (0.1), since (0.1) doesn't exist as a number, and makes me assume that you mean 0.(1), which is 0.111..., which is entirely different from 0.(0)1 or 0.000...1 that we're discussing.
To be clear, the () generally go around the part that is being repeated:
0.1 = 0.1
0.(1) = 0.111...
0.(0)1 = 0.000...1 (which most people would argue is impossible, as above, but for now I'm giving you the benefit of the doubt)
(0.1) = 0.10.10.10.1... (which obviously doesn't make sense, since you can't have an infinite number of decimals in a number, only 1)
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To Maelwys
Quote:
"
What do you mean "the calculation infinitely repeats itself"? Why can't I multiple the number 0.000...1? You told me that 0.000...1 / 2 = 0.000...5 up above, so if I can divide it "
A.R.B
Mainly because none of this has anything to do with Infinite Recurring Numbers!
my examples showed you from the start onwards! because we cant look at the end!!
Infinite Recurring ( n ) = n because! ( n ) will always = n
The above will always be true!
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Mainly because none of this has anything to do with Infinite Recurring Numbers!
Yes, it does, because you earlier defined 0.000...1 as the infinitely recurring number that represents the difference between 0.999... and 1. So I'm trying to establish the properties of 0.000...1 as a number to help me better understand the difference that it represents.
my examples showed you from the start onwards! because we cant look at the end!!
Why not? It ends with a ...0001, you already defined that above. So if we know where the end is, why can't we look at it?
Infinite Recurring ( n ) = n because! ( n ) will always = n
The above will always be true!
Can you please reformat the location of your ()s in accordance with the standard I explained in my above post, so I can better understand what you're saying?
Ex: 0.(n) = n, or 0.(n) = 0.n
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To Sekky
Quote: " start accepting basic facts about field theory "
A.R.B
I am more than sure!! the only field theory you really know about! is being in a field! with field mice!..
You are a child, good look getting a seat at any academic establishment with that attitude.
Also, your lack of knowledge will contribute to your academic failure, have fun!
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To Sekky
Quote:
" You are a child, good look getting a seat at any academic establishment with that attitude. "
A.R.B
Is the above ENGLISH!!
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To Maelwys
Where you are making mistakes! is you are trying to Calculate Infinite/Recurring Numbers/Values! as if they are Normal Numbers/Values!
If you really do believe Infinite/Recurring 0.9 never ends! then it must also be True for Any Infinite/Recurring Numbers/Values! what is True for one,must be True for all others!
The other thing you must accept is that all Numbers/Values have a Start!
Infinite/Recurring 0.9 " Starts as one Decimal place! "
Infinite/Recurring 0.1 " Starts as one Decimal place! "
Infinite/Recurring 0.1 + Infinite/Recurring 0.9 " Starts as one Decimal place! " and so from the Start onwards must always = 1
The two examples below will always run along side each other! as an Infinite Difference!
0.9999999999999999999999999999999999999999999999999999999999999999999999..........
0.0000000000000000000000000000000000000000000000000000000000000000000001..........
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Where you are making mistakes! is you are trying to Calculate Infinite/Recurring Numbers/Values! as if they are Normal Numbers/Values!
If you really do believe Infinite/Recurring 0.9 never ends! then it must also be True for Any Infinite/Recurring Numbers/Values! what is True for one,must be True for all others!
Okay, then yes I believe that for all cases, infinitely recurring numbers don't end, by definition.
The other thing you must accept is that all Numbers/Values have a Start!
Infinite/Recurring 0.9 " Starts as one Decimal place! "
Infinite/Recurring 0.1 " Starts as one Decimal place! "
Infinite/Recurring 0.1 + Infinite/Recurring 0.9 " Starts as one Decimal place! " and so from the Start onwards must always = 1
What number does "infinite/recurring 0.9" represent? (written out to 3 decimals is fine). What number does "infinite/recurring 0.1" represent? (again, to 3 decimals is fine)
What about 0.909090909090909090....? How do you represent that as starting as one decimal place?
The two examples below will always run along side each other! as an Infinite Difference!
0.9999999999999999999999999999999999999999999999999999999999999999999999..........
0.0000000000000000000000000000000000000000000000000000000000000000000001..........
What comes after the ... in this example?
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To Maelwys
Quote: "
What about 0.909090909090909090....? How do you represent that as starting as one decimal place? "
A.R.B
Ok for 0.909090909090909090....? " The starting decimal place! is the when the number changes in sequence! for the above it starts as 0.90
Quote: "
0.9999999999999999999999999999999999999999999999999999999999999999999999..........
0.0000000000000000000000000000000000000000000000000000000000000000000001..........
What comes after the ... in this example? "
A.R.B
It is always the Same! there is no after! the... as far as we can Calculate and show there will always be .999... and .001... both must be Infinite/Recurring!!
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Quote: "
0.9999999999999999999999999999999999999999999999999999999999999999999999..........
0.0000000000000000000000000000000000000000000000000000000000000000000001..........What comes after the ... in this example? "
A.R.B
It is always the Same! there is no after! the... as far as we can Calculate and show there will always be .999... and .001... both must be Infinite/Recurring!!
So where does the 1 go in the second number? If the 0s are infinite/recurring, always the same, with no after, then there's nowhere to put the 1.
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To Maelwys
Quote: "
So where does the 1 go in the second number? If the 0s are infinite/recurring, always the same, with no after, then there's nowhere to put the 1. "
A.R.B
The 1 does not go anywhere!
with 0.9999..... even though we can see many .9's we are in fact always looking at one .9
with 0.0001..... even though we can see many .0's we are in fact always looking at one .1
because .1 is the actual Infinite Difference! from the Start!
There has to be a Value between 0.9 and 0.1 and that is 0.000...the Decimal Shift!
The Infinite Difference does not Grow! is stays the same and is shifted!
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