Does 0.9 recuring = 1?

[Tobold]

0.3rec is a rational number, it can be written as the fraction

1
3

 

[Tobold]

tbh

 

[old.LandShark]

Do you agree 0.3rec. is 0.3 with an infinite number of 3's on the end?

Do you know the definition of infinity? (take any number; infinity is higher than it.)
1/3 is an exact quantity, which = 1 when multipled by 3.
1/3 as a decimal is 0.3 with an infinite number of 3's on the end. You can't perform operations on infinity; 0.3rec is not 1/3, it's merely an extremely good approximation of 1/3. 0.3rec.
Ergo 3*(1/3)=1 and 0.3rec. * 3 = 0.9rec. but 0.3rec. != 1/3

 

[Nightchill]

0.3rec is the decimal expansion (the representation of a number in base 10) of 1/3.

edit: there's been many papers published on this subject. it shouldn't be too difficult for you to find them if you're that interested.

 

[Tobold]

1/3 is an exact quantity, which = 1 when multipled by 3.
1/3 as a decimal is 0.3 with an infinite number of 3's on the end.

x=0.3rec 10x=3.3rec
9x=3.0
(9/9) or 1x=3/9 or 1/3
x=0.3rec and 1/3

thus proving that

0.3rec=1/3

 

[old.shotgunstow]

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 ;>

The explaination I offered is correct. 0.9 rec IS recurring to infinity. IF there is a limit on it, say it's only 0.9999999999999999999999 then it IS only 0.9999999999999999999999 NOT 1. But if it's 0.9rec, it IS 1.

Also referring to the calculator question:

I just took out my CASIO fx-83MS... did 1 / 3 then pressed equals:
0.3333 to end of calculator display.
Then pressed x3 = and it said: 1.

Point proven.

 

[old.shotgunstow]

Originally posted by old.LandShark
Do you agree 0.3rec. is 0.3 with an infinite number of 3's on the end?

Do you know the definition of infinity? (take any number; infinity is higher than it.)
1/3 is an exact quantity, which = 1 when multipled by 3.
1/3 as a decimal is 0.3 with an infinite number of 3's on the end. You can't perform operations on infinity; 0.3rec is not 1/3, it's merely an extremely good approximation of 1/3. 0.3rec.
Ergo 3*(1/3)=1 and 0.3rec. * 3 = 0.9rec. but 0.3rec. != 1/3

Wrong. 0.3 recurring as an infinite number of 3s on the end, IS equal to 1/3. It's only when there is a finite number of 3s that it is different.

 

[old.LandShark]

Thank you for demonstrating to me that x != x

 

[ChillyDawg]

0.9(rec) = 1

now be quiet, im trying to revise some useful maths for my A level!

 

[old.shotgunstow]

Originally posted by ChillyDawg
0.9(rec) = 1

now be quiet, im trying to revise some useful maths for my A level!

Me toooooo, well AS level ^_^

 

[old.shotgunstow]

btw if you want to use the != then yes I would agree, 0.9rec != 1.

 

[Nightchill]

1 last exam to go and i'm finished forever \o/ (astrophysics mphys)

 

[Danya]

Originally posted by old.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

Thus proving why seals are still stuck in the artic cold and the eskimos live in warm igloos.
3/10 = 0.3

 

[Aoln]

omg who cares?

 

[Spudgie]

Mathematics wizzes say 0.9rec is not equal to 1, whereas engineers who live in the real world say 0.9rec is 1 for practicallity.

 

[Tranquil-]

When it's recurring it tends to, it never becomes.

The reason calculators etc say 0.999999999999999999999999999999rec is = to 1 when you do some calcs on it is because there are no calculators that can handle a number of infinite size.

 

[old.Tohtori]

Then let's do the calculator thing with the most powerful calculator there is around...the windows calc!

0,3333333333333333333333333333333 *3 = ...yeah..you guessed it...0.9999999999999999999999999999999999999999

 

[Armalite]

0,9rec do NOT equal 1. The tiny difference is a VERY large difference when measuring distances between stars/planets/etc...

 

[Nightchill]

can't see when it would occur in astrophysics but eitherway, the factors in the hubble constant are usually the main uncertainties in any measurements at that scale.

 

[Tobold]

Originally posted by Armalite
0,9rec do NOT equal 1. The tiny difference is a VERY large difference when measuring distances between stars/planets/etc...

you what?
you understand what 0.9rec is?
infinate 9s, that means the gap is infinately small no matter what scale your talking about...

wait your taking the piss yeah?




tell me your taking the piss

 

[parlain]

Want to make your non-math head spin?

Try applying the concepts of transfinte cardinality and the hierarchy of different types of infinity utilising set theory and Cantor's Diagonal Theorem to the problem of defining what is "infinite" in the first place...