Does 0.9 recuring = 1?

[old.Tohtori]

Originally posted by Teh Krypt
STop it !

Theres no logic at all in the world as we know it to make 0.999999 (rec) = 1 .

0.99999(rec) is still a number.

Endless number.

Number nevertheless.

So..in a s-nes(sense) it is one number.

Ergo... 0.9999(rec) is = 1(number)

 

[gengi]

in a possibly finite universe, can there be an infinite number ? and if there is no infinity i.e the universe has an end will 0.9rec suddenly stop ? Can't remember the bloody theory but its a constant thing like planck's constant or avagardo's number which if it is <1 means the universe will eventually die back to the monbloc ground state, if it = 1 the universe continues expanding at a sustainable rate i.e time and the universe continue ad infinitum or if it>1 then the universe increases in volume to a point where it rips itself apart. I think it was in one of the popular cosmolgy books that i saw this particular theory and it probably has no bearing on the 0.9999 re thing.

Later

Gengee

 

[old.Dillinja]

It simply shows that the pathetic human numbering system which we have invented has many, many loopholes.

 

[Kharok Svark]

Bring infinity into any calculation and the rules change.

Infinity cannot be identified therefore you have a calculation issue.

The problem is recurring numbers, which were made up for decimilisation.

Mathematicians will always prefer fractions, they are logical.

 

[Tilda]

Originally posted by old.Psi
There was a formula or theory type thing we were told in school that (in theory) proved all recurring numbers were whole numbers...

It started with something like '66.66666 rec - 6.66666 rec = 60' and then went on from there if anyone wants to figure it out.

yes I remember something like that though. couldnt say exactally what it was though. But im sure that it ended up with 0.9rec = 1

Tilda

 

[the_fnord]

Ya'll made my head hurt.....

 

[Teh Krypt]

It can't tho



no matter how many 9's you put on, it will always be 0.9(+however many 9's) which is a different number to 1

 

[Tobold]

Originally posted by Tohtori
Then again...

0.333(rec)=3/10

0.666)rec)=6/10

Therefore 0.999(rec)=9/10

9/10 is not 10/10

Therefore 1 is not 0.999(rec)

unfortunately 0.333333rec is not 3/10 its 3/9
0.33333rec is 3.33333rec/10

therefore 0.99999rec = 9/9 or 1

 

[old.Psi]

Originally posted by Tobold
unfortunately 0.333333rec is not 3/10 its 3/9
0.33333rec is 3.33333rec/10

therefore 0.99999rec = 9/9 or 1

Try dividing 9 by 3 and see if it makes 3.3333rec.

Tohtori had it right.


And Krypt, this thing really did prove 0.9rec = 1, as I said we didn't really believe it as it was illogical but it did prove that it was.

 

[Tobold]

Originally posted by old.Psi
Try dividing 9 by 3 and see if it makes 3.3333rec.

um... i said

Originally posted by Tobold
unfortunately 0.333333rec is not 3/10 its 3/9.

thats 3 dividing by 9, not the other way round.
and i said it equaled 0.3rec, not 3.3rec

Originally posted by old.Psi
Tohtori had it right.

no he didn't

you sure you're reading what i wrote? :/

 

[Vell]

Mathematically .99999999999999999999..... = 1.

Whether you like it or not, whether it frazzles your brain or not, it's true.

So sayeth Vell the Wise.

 

[old.LandShark]

If someone has a mathematical proof that 0.9rec = 1, then I'd like to see it. So far only one has been offered and it was totally wrong since tending to infinity is not the same as being infinite ;>

 

[Easy]

Ok let's reason this way.

You have a pie. Right? One (1) pie to slice.
And you have 3 persons - you and two
other friends. Everyone wants an equal
part of the pie. So you <try> to slice it in
3 perfect parts.

Each one of those parts represents 33.3rec.%
of the pie itself. That is, 0.3rec. units of pie.

You still have one pie, it's just that you have
made 3 slices of it. But you started with one
pie nevertheless - it just changed form.

Here's a little quotation.

Originally discovered by Antoine Lavoisier:
Nothing is created and nothing is destroyed,
but everything is transformed.

The 1/3 operation looks like a true math
mystery. If you do the calculation 1/3, basically
your calculations never end, because you always
end up with a rest.

In other words: you just cannot stop dividing
- the operation never ends. Never. You will
ALWAYS end up with a <rest> as you progress
in your calculations.

Translation: it's possible to divide 1 by 3,
but you cannot <complete the operation>
by conventional means. To bypass this
problem, we have to resort to equations.

I'll rephrase that again: 1/3 is a real number,
it exists, but we lack the mathematical
skills to calculate it. But it exists
nevertheless, just like no part of
the one pie can be destroyed in the
slicing process.

So, let's resort to equations then.
Let's consider my previous solution
again.

Take the number

x = 0.9rec. (that would be 0.3rec. X 3)

Multiply by 100.

100x = 99.9rec.

Do a little math considering
the above results.

100x-x = 99.9rec. - 0.9rec.

So we have:

99 x = 99

There! We have bypassed
our mathematical problem
(the never-ending operation).

So,

x = 99/99 = 1

 

[old.Psi]

Hey, that's the one Easy !

And Tobold, I have no idea what I was thinking then, ignore it.

 

[Vell]

Originally posted by Old.Landshark
If someone has a mathematical proof that 0.9rec = 1, then I'd like to see it. So far only one has been offered and it was totally wrong since tending to infinity is not the same as being infinite ;>

Shotgunstow has already posted a proof.

Originally posted by old.shotgunstow
This little bit of maths theory is easily explained.

1/3 = 0.33333333333333333 recurring etc
2/3 = 0.66666666666666666 recurring etc
Therefore 3/3 = 0.999999999 recurring etc
And 3/3 = 1, therefore 0.999999 recurring = 1

Done

It's very very simple when you know how. Trust us maths boffins, it really does work.

 

[old.LandShark]

You maths boffins would presumably know that a rational number is any integer over any other integer? (p/q where q is not = 0, where p and q are integers)
0.3rec is NOT 1/3. Argument over. You have successfully proved that 99/99 = 1 (grats), and 3x (1/3) = 1 (grats again), but I'm afraid this doesn't prove 0.9rec = 1 because 0.3rec is not a third.

 

[Easy]

At the start of my example,

x = 0.9rec.

but at the end we have

x = 1

so because x = x (identity),

0.9rec. = 1

Ok?

 

[old.LandShark]

Ok? No.

You said yourself, 0.3rec is not a rational number. 1/3 IS a rational number. You shouldn't need me to tell you that, if you're a maths boffin :great:

(1/3)*3 = 1
Correct.
0.3rec * 3 = 0.9rec
Correct.

1/3 = 0.3rec
Wrong.


Feel free to correct me, but bear in mind that dancing around saying "stfu, non mathematical man!" won't work. Do not patronise me; repeating the conclusions of your argument does not prove them.

 

[Easy]

Originally posted by old.LandShark
0.3rec is not a rational number.

Yea, I said that,
I corrected that because it was a mistake. But I simply
used the wrong word - that's all. A typo.

maths boffin

Loaded language.

1/3 = 0.3rec
Wrong.

Ok, what do you end up with if you do 1/3 on the calculator.

dancing around saying "stfu, non mathematical man!" won't work.

Huh? I am not that kind of person. If you think that I would act like that, you are definitely wrong in this.

repeating the conclusions of your argument does not prove them.

Of course. Show me The Way then.

 

[Kharok Svark]

As I said earlier, if you want pure maths without the get out clause of recurring for decimalisation, use fractions.

 

[old.LandShark]

Originally posted by Easy
Yea, I said that,
I corrected that because it was a mistake. But I simply
used the wrong word - that's all. A typo.
Are you, then, saying that 0.3recurring IS a rational number? Cos the first one was right. Any recurring number IS irrational.

Loaded language.
Vell's words, not yours or mine

Ok, what do you end up with if you do 1/3 on the calculator.
I end up with the finite number 0.33333333, which isn't correct but it's as near as my poor calculator can get.

Huh? I am not that kind of person. If you think that I would act like that, you are definitely wrong in this.
Well, don't take it too hard, you know. I've seen too many moderately intelligent debates turn into that crap - wasn't accusing you particularly.

Right.

My point was that 0.3rec. is not a rational number, whereas 1/3 IS a rational number.

It's not complicated;
If x is not zero, 1-x cannot be 1.
Are you telling me 1-0 = 0.9rec. ?

 

[Pin]

no. 0.9recurring != 1

 

[old.LandShark]

Yus. That much is totally obvious, tbh... I'm just having fun indicating the flaws in the logic :>

 

[Pin]

well all you asked for is me to agree with you

 

[old.LandShark]

Well, now I'm asking you if I'm wrong, lol

 

[Easy]

Originally posted by old.LandShark
Are you, then, saying that 0.3recurring IS a rational number?

No. Simply that I corrected a mistake. Sometimes,
typos are made. That's all...

Ok, what do you end up with if you do 1/3 on the calculator.

I end up with the finite number 0.33333333, which isn't correct but it's as near as my poor calculator can get.

#1. Do 1/3 on the calculator, then multiply the result by 3. Note
the result.

#2. After that, clean the display and do 0.33333333 X 3. Note
the result.

Tell me what results you get in cases #1 and #2.

Are you telling me 1-0 = 0.9rec. ?

If 1=0.9rec. , probably also 1-0 = 0.9rec. would be true?
What do you think about it?

 

[old.LandShark]

Originally posted by Easy
If 1=0.9rec. , probably also 1-0 = 0.9rec. would be true?
What do you think about it?

Guh... Your premise is incorrect; 1 != 0.9rec.
I am not arguing in some fantasy world where x != x, you needn't restate your incorrect conclusion as if I was incapable of understanding it the first two times.

0.3rec. is irrational, 1/3 is rational, ergo 0.3rec. != 1/3, ergo 3*0.3rec. != 1

Originally posted by Easy
#1. Do 1/3 on the calculator, then multiply the result by 3. Note
the result.

#2. After that, clean the display and do 0.33333333 X 3. Note
the result.

If i ask my calculator what 3(1/3) is, it tells me 1. Not particularly surprised.
If i ask my calculator what 0.33333333 * 3 is, I get 0.99999999.
Where's your point?

 

[Easy]

Originally posted by old.LandShark
If i ask my calculator what 3(1/3) is, it tells me 1. Not particularly surprised.
If i ask my calculator what 0.33333333 * 3 is, I get 0.99999999.
Where's your point?

Ok, what do you end up with if you do 1/3 on the calculator.

I end up with the finite number 0.33333333,
which isn't correct but it's as near as my poor calculator can
get.

If you really end up with a finite number like you stated above,
why do the two results differ?

 

[old.LandShark]

Because a third is not equal to 0.3recurring.
Which was my original point. Which so far you only seem to be agreeing with, even though it renders your own original proof invalid.

 

[nalistah]

0.9999etc to eternity could never equal 1... its always a little bit missing... sure... its not much.. but always something