0.9999999...... = 1

[Frutos]

Interesting article on Wikipedia today:

Instead of working on defining what does or does not equal 1, perhaps you could explain for me your definition of 'interesting'.

 

[Biscuit]

QUICK,

ITV NOW..

PAINT DRYING LIVE!

 

[*Gullsworth*]

1+1=2 Anyone?..................................

 

[Robdinho]

I always though that if you divide anything by 0 you get infinity!

Something divided by 0 is not infinity as that would mean that 0 multiplied by infinity equalled something. And it doesn't, it's still 0.

 

[Artois]

QUICK,

ITV NOW..

PAINT DRYING LIVE!

Quick.

Stop being a twat.

 

[Tesco in Disguise]

QUICK,

ITV NOW..

PAINT DRYING LIVE!

just because you don't undersatnd something, doesn't make it wrong.

 

[DTES]

Not bonkers at all, simply incorrect and flawed maths. Either deliberatley or accidentally.

The numbers .9999999999..... and .33333333333..... are infinite sequences. Therefore the equation

c = 0.999…
10c = 9.999…
10c − c = 9.999… − 0.999…
is invalid at the following.
9c = 9
The correct answer to the above is
9c = 9.0000000000000................... to infinity where the last number in the sequence (which there isn't because itis infinite) is 1.

Hence c = 1 is an invalid and flawed conclusion. You can legitimately write C is approximately= 1 but the exact is not correct.

Wow, I didn't think my degree in Maths would ever help on NSC...

But, yes, 0.9999999999....... does equal 1. The argument I've quoted isn't correct because quite simply (as you've said), there is no last number in the sequence.

It's the same principle in practice as the proof that there are an identical number of rational numbers as there are natural numbers (where each natural number is 'paired off' with a rational number), here each figure in c is paired off with a figure after the decimal place in 10c.

There is then no decimal places in c which are not present in 10c, and hence 10c - c = 9. Exactly 9.

(You know, it's that bad here in the office this week that this has made my day. If only I could go back to studying...)

 

[Buzzer]

Re: Re: 0.9999999...... = 1

Yes, another proof is 0.33..... = 1/3

1/3 x 3 = 1

0.33..... x 3 = 0.99.....

Therefore 0.99.... = 1

incorrect in line 2

0.33..... x 3 = 1

As with all the other people who have blown these calculations out the water, it's all in the roundings.

 

[Tom Hark Preston Park]

We had a number called 'the square root of minus one' when I was at school. Think I lost all interest in maths round about then...

 

[Herr Tubthumper]

I think you'll find you're wrong.

It's certainly what I was taught at University all those years ago.

I know it's not always the most reliable source in the World, but
here's Wikipedia's take on it. This article cites very reliable references.

Fork Me

Why is he wrong? I've got a degree in maths and I'll tell you that 0.9999999 recurring isnt equal to one (although this is so elementary you only need a bit of schooling to appreciate 0.999 ne 1). The limit tends to one infinately but nothing else.

 

[Buzzer]

We had a number called 'the square root of minus one' when I was at school. Think I lost all interest in maths round about then...

*nods head*
Aye



(see what I did there?)

 

[DTES]

We had a number called 'the square root of minus one' when I was at school. Think I lost all interest in maths round about then...

Yep. (-1)^0.5 = i

Sounds crazy, but space flight wouldn't be possible without it. Engineering (and quantum physics for that matter) depends on it's existence to solve a lot of their respective equations...

 

[Buzzer]

Why is he wrong? I've got a degree in maths and I'll tell you that 0.9999999 recurring isnt equal to one (although this is so elementary you only need a bit of schooling to appreciate 0.999 ne 1). The limit tends to one infinately but nothing else.

what he said.

except I've only got a degree in theoretical nuclear physics, so the maths wasn't quite so hard and we could make assumptions such as 0.9999 recurring = 1.


We could also make assumptions such as 'assume g=0' which used to piss off the engineers but that's another story.

 

[Herr Tubthumper]

Yep. (-1)^0.5 = i

Sounds crazy, but space flight wouldn't be possible without it. Engineering (and quantum physics for that matter) depends on it's existence to solve a lot of their respective equations...

Imaginary numbers, a great topic. That's when my interest in maths increased.

 

[Tom Hark Preston Park]

Yep. (-1)^0.5 = i

Sounds crazy, but space flight wouldn't be possible without it.

Would that be imaginary space flight by any chance?

 

[DTES]

Right, if anyone out there is still somehow not convinced of the fact that they are equal, here is another proof, even more watertight:

1. You can write 0.99999999r = 0.9 + 0.09 + 0.009 + 0.0009....

Then using standard geometric summation (which unfortunately I can't use proper notation for in this, but imagine the symbols idf you will...)

Using a = 0.9, r = 0.1 we have

Sn = a + ar + ar^2 + ar^3 + .....
= a / (1-r)
=0.9 / (1-0.1)
=1




(Call me a geek all you want, but you can't say I'm wrong...)

 

[DTES]

Would that be imaginary space flight by any chance?

No.

Unless you're one of these conspiracy theorists that thinks we've never actually been there, and it's all in a NASA studio.

 

[chip]

Right, if anyone out there is still somehow not convinced of the fact that they are equal, here is another proof, even more watertight:

1. You can write 0.99999999r = 0.9 + 0.09 + 0.009 + 0.0009....

Then using standard geometric summation (which unfortunately I can't use proper notation for in this, but imagine the symbols idf you will...)

Using a = 0.9, r = 0.1 we have

Sn = a + ar + ar^2 + ar^3 + .....
= a / (1-r)
=0.9 / (1-0.1)
=1




(Call me a geek all you want, but you can't say I'm wrong...)

Ah, but be careful here. Series expansions such as these, or Taylor expansions, Hilbert spaces, Li algebra etc. are only approxinmations of the original (nonlinear/unknown) function. In a pre-principia mathematica age you might be correct, now you would surely have to bound the universe of discourse?

GEEK

 

[Herr Tubthumper]

what he said.

except I've only got a degree in theoretical nuclear physics, so the maths wasn't quite so hard and we could make assumptions such as 0.9999 recurring = 1.


We could also make assumptions such as 'assume g=0' which used to piss off the engineers but that's another story.

For practical and applied reasons I am sure you can assume it is 1 in certain circumstances....but technically it is not.

 

[Buzzer]

For practical and applied reasons I am sure you can assume it is 1 in certain circumstances....but technically it is not.

Because the stuff was all theoretical we could ignore the effects of real life. A bit like when making calculations involving pendulums. The engineer would have to worry about the resistance caused by not being in a vacuum and also at the point at which the pendulum swings (the fulcrum?) whereas the theoretical physicist would say, 'oh well, for the purposes of this calculation I'll just assume......'

The maths required becomes much easier that way!

*shudder* I've just remembered trying to learn Maxwell's Equations by rote!