0.99999... = 1

Harrypotter_fan

Harrypotter_fan

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I'm really confused about this. It can be proved that 0.99999... is equal to 1.

We know that,
(1 / 3) = 0.33333...
Multiplying both sides by 3,
1 = 0.99999...

But the difference between 1 and (0.99999...) is (0.00000...1).
And that implies that (0.00000...1) = 0.
 
Last edited:
Your logic is flawed. 1/3 != 0.3333, meaning not equal to. It ends up to an infinite digits, which effectively changes its values.
Also, difference between 0.9999 and 1 is not 0.1111, its 0.000000.... and a 1 in the last which you can't define.

And therefore, they both have difference. Although just for making things easier we approximate them. You can't multiply 3 to a number you can't fully define, for e.g 0.33333.... because it has no end! Its a non terminating decimal...

Its the same as multiplying both sides by 0. :p
 
barmyarmy said:
Actually 0.0 recurring 1. i.e. 0.999 + 0.111 <> 1; 0.999 + 0.001 = 1
Click to expand...

Yes, I know that, it was just a mistake while typing it. Thanks for the wiki article Matt.

Harrypotter_fan added 12 Minutes and 16 Seconds later...

Kshitiz_Indian said:
Your logic is flawed. 1/3 != 0.3333, meaning not equal to. It ends up to an infinite digits, which effectively changes its values.
Also, difference between 0.9999 and 1 is not 0.1111, its 0.000000.... and a 1 in the last which you can't define.

And therefore, they both have difference. Although just for making things easier we approximate them. You can't multiply 3 to a number you can't fully define, for e.g 0.33333.... because it has no end! Its a non terminating decimal...

Its the same as multiplying both sides by 0. :p
Click to expand...

We can multiply non-terminating decimals. And 3 times 0.333... does equal 0.999....
 
Yes, it equals to 99999999999999999999999999999999999999999999999999999999999... as many times as your screen feels fit. But then you're multiplying an infinite number, something I think is a loophole of mathematics, just like dividing anything by zero.
 
It isn't really a loophole of mathematics. 1/3 is not 0.333333333333333333333333333. The threes keep going infinitely, meaning it is a number which can not be fully written as other numbers can. Therefore it is most accurately written 1/3. 1/3 x 3 is 1.

0.999... could be written as a sequence where it is 0.9 + 0.09 + 0.009 + ..., and as the sequence goes on the number gets closer and closer to being 1. (or has an asymptote of 1) Do it infinity times, and you actually have 1. Therefore 0.999... = 1
 
But then infinity times doesn't have a proper definition. You could do it a million times and say its the closest to one, and I would do it another billion times and say its much closer now, and so on. There's no end to it!
 
tassietiger said:
It isn't really a loophole of mathematics. 1/3 is not 0.333333333333333333333333333. The threes keep going infinitely, meaning it is a number which can not be fully written as other numbers can. Therefore it is most accurately written 1/3. 1/3 x 3 is 1.

0.999... could be written as a sequence where it is 0.9 + 0.09 + 0.009 + ..., and as the sequence goes on the number gets closer and closer to being 1. (or has an asymptote of 1) Do it infinity times, and you actually have 1. Therefore 0.999... = 1
Click to expand...

Doing it infinitely won't make it one. It will just come closer to one.
 
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