Ok. Is 0.0(repeating)1 a number?
If you try to think of the smallest number possible above zero, you come to this conclusion. Yet, if you try to add it together, it will never amount to anything greater than itself because it is an infinitely small decimal place. Basically, this number is zero?
so 0.0(repeating)1 = 0?
and does 0.0(repeating)2 = 0 also?
IF you take out your calculator you can see the number I am talking about by typing in 1/3 then multiplying that by 3, and you get 0.9(repeating) not 1. So, this difference is so small it is nothing? it isn't a difference at all just a different representation of the same number?
Originally posted by ChessJesterIf you print out lottery tickets with 0.0 chance of winning, no one will buy one. If you sell lottery tickets with a 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 chance of winning, lots of people will buy because no matter how remote that chance is, no matter how tiny the number, there is still the possibility of winning.
Ok. Is 0.0(repeating)1 a number?
If you try to think of the smallest number possible above zero, you come to this conclusion. Yet, if you try to add it together, it will never amount to anything greater than itself because it is an infinitely small decimal place. Basically, this number is zero?
so 0.0(repeating)1 = 0?
and does 0.0(repeating)2 = ...[text shortened]... it is nothing? it isn't a difference at all just a different representation of the same number?
Originally posted by ChessJester.999999999999999999999999999999999999999999999999999 < 1
Ok. Is 0.0(repeating)1 a number?
If you try to think of the smallest number possible above zero, you come to this conclusion. Yet, if you try to add it together, it will never amount to anything greater than itself because it is an infinitely small decimal place. Basically, this number is zero?
so 0.0(repeating)1 = 0?
and does 0.0(repeating)2 = ...[text shortened]... it is nothing? it isn't a difference at all just a different representation of the same number?
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Originally posted by ChessJesterI think this is a good example of the concept of infinity.
Ok. Is 0.0(repeating)1 a number?
If you try to think of the smallest number possible above zero, you come to this conclusion. Yet, if you try to add it together, it will never amount to anything greater than itself because it is an infinitely small decimal place. Basically, this number is zero?
so 0.0(repeating)1 = 0?
and does 0.0(repeating)2 = ...[text shortened]... it is nothing? it isn't a difference at all just a different representation of the same number?
You can insert as many zeros as you wish prior to the 1. It will always be a greater number than zero, but the more you add, the infinitely closer to zero it becomes.
So to answer your question, yes it will always be a number, no matter how far you go with it. As soon as you define the number of zeros before the one, you define the number, which is greater than zero.
Your calculator is pretty pathetic in the face of such numbers. But if you add an almost incalculably small number to another one, it is still greater than either sum.
Originally posted by ChessJester'Posers and Puzzles' Posters should be here to look at your question.
Ok. Is 0.0(repeating)1 a number?
If you try to think of the smallest number possible above zero, you come to this conclusion. Yet, if you try to add it together, it will never amount to anything greater than itself because it is an infinitely small decimal place. Basically, this number is zero?
so 0.0(repeating)1 = 0?
and does 0.0(repeating)2 = ...[text shortened]... it is nothing? it isn't a difference at all just a different representation of the same number?
1 edit
Originally posted by PolicestateI always thought that time (for example one second) can be divided into infinite little parts. But recently I've read that there are smallest time parts from whom the timeline is made. Like for example approx. 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 seconds, or similar. So, time in our space is like movie with say 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 frames per second instead of classic 24 frames or little more for a Hollywood movie. I know this is a bit of topic but how that can be possible ?
I think this is a good example of the concept of infinity.
You can insert as many zeros as you wish prior to the 1. It will always be a greater number than zero, but the more you add, the infinitely closer to zero it becomes.
So to answer your question, yes it will always be a number, no matter how far you go with it. As soon as you define the number ...[text shortened]... you add an almost incalculably small number to another one, it is still greater than either sum.
Particle, smallest unit of time that can not be divided ??
2 edits
Originally posted by ChessJesterIs 0.0(repeating)1 a number?
Ok. Is 0.0(repeating)1 a number?
If you try to think of the smallest number possible above zero, you come to this conclusion. Yet, if you try to add it together, it will never amount to anything greater than itself because it is an infinitely small decimal place. Basically, this number is zero?
so 0.0(repeating)1 = 0?
and does 0.0(repeating)2 = ...[text shortened]... it is nothing? it isn't a difference at all just a different representation of the same number?
No.
If you try to think of the smallest number possible above zero, you come to this conclusion.
But that's not a number. There is no smallest number possible above zero. If you find a candidate, try dividing it by ten and you'll see it is not the smallest after all.
The correct way to express what you are saying, I think, is the limit of 10^(-n) as n approaches infinity. That limit is zero.
Originally posted by ChessJesterIt's a bit ambiguous. Here's a quote from a Wikipedia article on infinitessimals:
Ok. Is 0.0(repeating)1 a number?
If you try to think of the smallest number possible above zero, you come to this conclusion. Yet, if you try to add it together, it will never amount to anything greater than itself because it is an infinitely small decimal place. Basically, this number is zero?
so 0.0(repeating)1 = 0?
and does 0.0(repeating)2 = ...[text shortened]... it is nothing? it isn't a difference at all just a different representation of the same number?
"The naive definition of an infinitesimal is this: a number whose absolute value is less than any non-zero positive number. From this definition, it can be shown than there are no non-zero real infinitesimals, using the property of the least upper bound."
http://en.wikipedia.org/wiki/Infinitesimal
However, the same article refers to the use of infinitessimals in alternative real number systems:
"Despite this, the real numbers can in fact be extended and modified to include infinitesimals, forming such systems as the dual numbers or the hyperreals, but this can only be done if certain properties of the real numbers are removed."
So 0.0000...1 seems to be a number, but not in the system we're used to.
Originally posted by AThousandYoungnice!
[b]Is 0.0(repeating)1 a number?
No.
If you try to think of the smallest number possible above zero, you come to this conclusion.
But that's not a number. There is no spallest number possible above zero. If you find a candidate, try dividing it by ten and you'll see it is not the smallest after all.
The correct way to express w ...[text shortened]... ou are saying, I think, is the limit of 10^(-n) as n approaches infinity. That limit is zero.[/b]
Ok, so there is no way to conceive of the smallest number above zero?
"no matter where you go, there you are" kind of thing?
DEEP!
3 edits
Originally posted by ivan2908Simple algebra will demonstrate it, no calculus needed. Here's the proof:
I do not believe that ! Maybe it is just becoming infinitely close to 1 but it's still not 1. 😕
.9999.....= 1
10(.99999....)= 10 (1) Multiply each side by ten, you get:
9.9999...... = 10 Then subract 9 from each side
9.999999.... -9 = 10 - 9
.999999......= 1
Learned that in the 7th grade. Your problem Ivan is you're thinking in finite terms, the infinite expansion of .99999...... makes the limit of the expression equal to 1.
It works even better with 1/3 = .3333333.....
3 (1/3) = 3 (.333333.....) (multiply each side by 3)
1 = .999999999........
Originally posted by Sam The ShamTry hitting the moon with a ship replacing .9999999999999999999999872 with 1.
Simple algebra will demonstrate it, no calculus needed. Here's the proof:
.9999.....= 1
10(.99999....)= 10 (1) Multiply each side by ten, you get:
9.9999...... = 10 Then subract 9 from each side
9.999999.... -9 = 10 - 9
.999999......= 1
Learned that in the 7th grade. Your problem Ivan is you're thinking in finite terms, the infini ...[text shortened]... 33333.....
3 (1/3) = 3 (.333333.....) (multiply each side by 3)
1 = .999999999........
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