yesh yesh!
0.99999... = 1
- Thread starter Harrypotter_fan
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yesh yesh!
Kshitiz_Indian
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I have to side by what Rob said, and I've been trying to say the same thing for the last 10 pages. They might be taken same approximately and might actually lead to no calculation errors in most cases, but mathematically they're not supposed to be equal.
Harrypotter_fan
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Can you answer my question?
Kshitiz_Indian
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Hang on, reading through earlier this thread I came across a post saying that 0.9999... is equal to one because as we would keep adding infinite 9's in it, it would sometime be so close to one that it'll be one.
I could add this to 0.3333... too. Everytime we would add a 3 it gets closer to one, because 0.33>0.3 and so on. So as we would add infinite nines it would also keep getting closer and closer and closer and closer to one, but we don't call 0.333... one do we?
I could add this to 0.3333... too. Everytime we would add a 3 it gets closer to one, because 0.33>0.3 and so on. So as we would add infinite nines it would also keep getting closer and closer and closer and closer to one, but we don't call 0.333... one do we?
Harrypotter_fan
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Can the non believers answer my question of representing it as p/q?
Kshitiz_Indian
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Can you answer my question in the last post?
Harrypotter_fan
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Yes. Try using geometric progression and you will get the answer yourself.
tassietiger
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Okay, this has annoyed me enough now.
Think of 0.999... as a sequence which is 0.9 + 0.09 + 0.009 + ...
The first number is 0.9, and the ratio of one term to the next term is 1/10 (or 0.1)
The sum of a sequence to infinity is:
the first term / (1 - the ratio of one term to the next)
or a / (1 - r)
This is the tricky bit to get your head around, but I've tried making it simpler and it hasn't worked.
If a = 0.9, and r = 0.1
0.999... = 0.9 + 0.09 + 0.009 ... = a / (1 - r) = 0.9 / (1 - 0.1) = 0.9 / 0.9 = 1
tassietiger added 1 Minutes and 49 Seconds later...
The difference between 0.333... and 1 is 0.666... The difference between 0.999... and 1 is 0.000... You took that comment too literally.
Think of 0.999... as a sequence which is 0.9 + 0.09 + 0.009 + ...
The first number is 0.9, and the ratio of one term to the next term is 1/10 (or 0.1)
The sum of a sequence to infinity is:
the first term / (1 - the ratio of one term to the next)
or a / (1 - r)
This is the tricky bit to get your head around, but I've tried making it simpler and it hasn't worked.
If a = 0.9, and r = 0.1
0.999... = 0.9 + 0.09 + 0.009 ... = a / (1 - r) = 0.9 / (1 - 0.1) = 0.9 / 0.9 = 1
tassietiger added 1 Minutes and 49 Seconds later...
The difference between 0.333... and 1 is 0.666... The difference between 0.999... and 1 is 0.000... You took that comment too literally.
Kshitiz_Indian
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tassietiger said:
Yes, but infinite means infinite, and if its infinite it has no end. So a difference of 0.666... too can be achieved by infinite 3's, since infinite actually has no end.
Harrypotter_fan
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G.M. explains it well enough.
That is accepted in the matsh world, but it isn't an exact difference, because there is none when 0.333...is infinite. If it is just 0.333 then the difference is 0.667, but the difference between 0.333... and 1 doesn't exist, technically.
Harrypotter_fan
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The difference between it is 2/3.
Kshitiz_Indian
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The difference between 1 and 1/3 is 2/3, yes. But not 0.333... and 1.000...
Also, if 1 = 0.999.... then 1-0.9999 = 0
But 1 - 0.99.... = 0.000..... and in the end a 1, since most of you have imagined an end to infinity anyways.
Also, if 1 = 0.999.... then 1-0.9999 = 0
But 1 - 0.99.... = 0.000..... and in the end a 1, since most of you have imagined an end to infinity anyways.
Harrypotter_fan
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you can't say infinite zeros and then 1
:. There is nothing after infinite, or it wouldn't be infinite.
Kshitiz_Indian
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And there is no end to infinite either, and that's why its called infinite. Isn't it? Then the very theory of infinite 9's getting sometimes equal to 1 is proven wrong!you can't say infinite zeros and then 1
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