Is 1 = 0.9999......

[zippy]

Originally posted by: flood
1/3 = 0.3333...

1/3 + 1/3 + 1/3 = 1
0.3333... + 0.3333... + 0.3333... = 0.9999...

1 = 0.9999...

 

[TuxDave]

That proof looks good to me. I believe 0.9999... = 1. For those who don't believe still, show me 1-0.999... doesn't equal 0. 🙂

And if you say it equals 0.000000.....001... there's an infinite number of zeros, so that '1' never really exists, so technically 1-0.999... = 0

 

[spidey07]

Contains the series and actual proof

http://mathforum.org/dr.math/faq/faq.0.9999.html

 

[Haircut]

Originally posted by: Zakath15
Yes and no. For all intents and purposed, 0.999999.... is 1. (0.9999999... eventually converges to 1)

No.
0.9999... is 1, it doesn't converge to anything.

The series:

Sum [i = 1 to n] 9 * 0.1^i

converges to 1 as n tends to infinity.

 

[Czar]

Originally posted by: Haircut

Originally posted by: Czar
1.000000000000000000000000000000000000000000000000000000000000000...... = 1
0.999999999999999999999999999999999999999999999999999999999999999...... ~= 1

just depends how you round it
its like saying that 1/3 is the same as 0.3, which it isnt

This has nothing to do with rounding, approximate answers or anything like that.
0.999.... is the same number as 1.

There are other ways to prove it that the one shown here, but it doesn't change the fact that they are two ways of writing the same number.

this has everything to do with rounding
is 0.3333... the same as 0.3 ?

 

[NuclearFusi0n]

yes, .9 repeating equals 1.

 

[Kyteland]

Originally posted by: spidey07
Contains the series and actual proof

http://mathforum.org/dr.math/faq/faq.0.9999.html

I actually showed that same proof to two of my coworkers earlier and they said that the limits thing is still an approximation because the summation never terminates.

I think they are full of it.

 

[TuxDave]

Originally posted by: Czar

Originally posted by: Haircut

Originally posted by: Czar
1.000000000000000000000000000000000000000000000000000000000000000...... = 1
0.999999999999999999999999999999999999999999999999999999999999999...... ~= 1

just depends how you round it
its like saying that 1/3 is the same as 0.3, which it isnt

This has nothing to do with rounding, approximate answers or anything like that.
0.999.... is the same number as 1.

There are other ways to prove it that the one shown here, but it doesn't change the fact that they are two ways of writing the same number.

this has everything to do with rounding
is 0.3333... the same as 0.3 ?

No it's not, but we're claiming 0.333.... = 1/3, that's different

 

[BruinEd03]

Originally posted by: Kyteland

Originally posted by: spidey07
Contains the series and actual proof

http://mathforum.org/dr.math/faq/faq.0.9999.html

I actually showed that same proof to two of my coworkers earlier and they said that the limits thing is still an approximation because the summation never terminates.

I think they are full of it.

Congratulations, your co-workers have just destroyed the foundation for caclulus 🙂

-Ed

 

[spidey07]

Your friends at work don't understand basic calculus and number systems then.

🙂

 

[Orsorum]

Originally posted by: Haircut

Originally posted by: Zakath15
Yes and no. For all intents and purposed, 0.999999.... is 1. (0.9999999... eventually converges to 1)

No.
0.9999... is 1, it doesn't converge to anything.

The series:

Sum [i = 1 to n] 9 * 0.1^i

converges to 1 as n tends to infinity.

Bad terminology on my part... I'll explain something or other later (after I'm done watching the Simpsons). 😀

 

[Haircut]

Originally posted by: Czar

Originally posted by: Haircut

Originally posted by: Czar
1.000000000000000000000000000000000000000000000000000000000000000...... = 1
0.999999999999999999999999999999999999999999999999999999999999999...... ~= 1

just depends how you round it
its like saying that 1/3 is the same as 0.3, which it isnt

This has nothing to do with rounding, approximate answers or anything like that.
0.999.... is the same number as 1.

There are other ways to prove it that the one shown here, but it doesn't change the fact that they are two ways of writing the same number.

this has everything to do with rounding
is 0.3333... the same as 0.3 ?

No, clearly it isn't.
When we are talking about an infinite number of 9s however, it isn't that the number rounds up to 1, it is actually 1.

 

[bleeb]

Originally posted by: spidey07
Contains the series and actual proof

http://mathforum.org/dr.math/faq/faq.0.9999.html

BAH HUMBUG.... Sounds like heresy to me.


they are losing the precision by messing with fractions rather than pure decimals. ifyou stick with decimals... even till the digits to the right of the decimal reach infinity... it still going to be 0.9999999999999 and not exactly 1.

 

[spidey07]

bwahahahahaa

Nice one BruinEd!!

 

[Czar]

actually after reading http://mathforum.org/library/drmath/view/57040.html this, it got me thinking

if 1/3 + 1/3 + 1/3 = 1 then how come 0.333... + 0.333... + 0.333... = 1 ?

both are right in my opninion

 

[spidey07]

bleep,

you can believe what you want. 🙂

But there really isn't any debate to this.

They are the same number. Just as 1 + 1 = 2. (or 1.999...)

 

[TuxDave]

Originally posted by: Czar
actually after reading http://mathforum.org/library/drmath/view/57040.html this, it got me thinking

if 1/3 + 1/3 + 1/3 = 1 then how come 0.333... + 0.333... + 0.333... = 1 ?

both are right in my opninion

Because 1/3 = 0.333...?

 

[bleeb]

its bleeb

 

[Czar]

Originally posted by: TuxDave

Originally posted by: Czar
actually after reading http://mathforum.org/library/drmath/view/57040.html this, it got me thinking

if 1/3 + 1/3 + 1/3 = 1 then how come 0.333... + 0.333... + 0.333... = 1 ?

both are right in my opninion

Because 1/3 = 0.333...?

yes

 

[spidey07]

Originally posted by: bleeb
its bleeb

😱

 

[bleeb]

But anyways... is the same proof recognized by all the mathematical societies? who is the "last word" on this particular subject?

 

[Czar]

Originally posted by: bleeb
But anyways... is the same proof recognized by all the mathematical societies? who is the "last word" on this particular subject?

the Anandtech Moderator probably 😉

 

[TuxDave]

Originally posted by: bleeb
But anyways... is the same proof recognized by all the mathematical societies? who is the "last word" on this particular subject?

There's bound to be a society that disagrees with something. I was in a logic class one day and this is what one particular society believed.

Given:
If you live in London, you get $100
If you don't live in London, you get $100

Now they completely believed that if you didn't tell them where you lived, they cannot tell you if you get $100. 0_o

 

[bleeb]

Originally posted by: TuxDave

Originally posted by: bleeb
But anyways... is the same proof recognized by all the mathematical societies? who is the "last word" on this particular subject?

There's bound to be a society that disagrees with something. I was in a logic class one day and this is what one particular society believed.

Given:
If you live in London, you get $100
If you don't live in London, you get $100

Now they completely believed that if you didn't tell them where you lived, they cannot tell you if you get $100. 0_o

EXACTLY MY POINT.

 

[TuxDave]

Looking at the polls... there seems to still be lots of ppl who disagree...