0.9999999...... = 1

[Artois]

Interesting article on Wikipedia today:

The gist of it being:

c = 0.999…
10c = 9.999…
10c − c = 9.999… − 0.999…
9c = 9
c = 1







Yes, I'm bored at work.

 

[Commander]

Racist.

 

[The Clown of Pevensey Bay]

Just been looking at that.

0.9999... divide 3 is 0.33333333.... is one third.

three thirds = 1.

Bonkers.

 

[sparkie]

Rounding error.

 

[readingstockport]

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.

 

[The Antikythera Mechanism]

Any Number Equals Its Own Double


We start with a statement of equality
a = b

We then multiply both sides by the value, a
a2 = ab

Subtract b2 from both sides
a2 - b2 = ab - b2

Factor both sides
(a+b)(a-b) = b(a-b)

Now divide both sides by the same value, a-b
(a+b) = b

Substitute a with its equivalent value, b.
2b = b

 

[Bad Ash]

Now divide both sides by the same value, a-b
(a+b) = b

a-b = a-a = 0

You cannot divide by zero. That's where most 'proofs' like this fall apart.

 

[Mark Ormerod's Gloves]

serious geekage

 

[NMH]

Are you Adri, are you adri, aaaare you adri in disguuuiiiise.....

 

[fork me]

Interesting article on Wikipedia today:

The gist of it being:

c = 0.999…
10c = 9.999…
10c − c = 9.999… − 0.999…
9c = 9
c = 1







Yes, I'm bored at work.

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

1/3 x 3 = 1

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

Therefore 0.99.... = 1

 

[fork me]

Rounding error.

No, there is no error, it is accepted by mathematicians that 0.99..... (meaning 0.9 recurring or 0.999999999 going on forever with no end) is equal to one.

Fork me

 

[Lammy]

Any Number Equals Its Own Double


We start with a statement of equality
a = b

We then multiply both sides by the value, a
a2 = ab

Subtract b2 from both sides
a2 - b2 = ab - b2

Factor both sides
(a+b)(a-b) = b(a-b)

Now divide both sides by the same value, a-b
(a+b) = b

Substitute a with its equivalent value, b.
2b = b

this works if a & b = 0

 

[readingstockport]

No, there is no error, it is accepted by mathematicians that 0.99..... (meaning 0.9 recurring or 0.999999999 going on forever with no end) is equal to one.

Fork me

Bollocks. NO mathematician anywhere will EVER accept that 0.99.... recurring is equal to one. They will accept that it is approximately equal to one but in mathematics and physical sciences the term eqaulity means EXACTLY what it says on the tin. EQUALITY. They are EXACTLY equal.

0.999........ is not and never ever will be equal to 1.

 

[readingstockport]

this works if a & b = 0

No, you can not divide by 0.

 

[Seagull Stew]

No, you can not divide by 0.

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

 

[readingstockport]

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

You do sort of but in reality it is a meaningless exercise in mathematics since the actual result of the calculation is not computable.

 

[Artois]

Bollocks. NO mathematician anywhere will EVER accept that 0.99.... recurring is equal to one. They will accept that it is approximately equal to one but in mathematics and physical sciences the term eqaulity means EXACTLY what it says on the tin. EQUALITY. They are EXACTLY equal.

0.999........ is not and never ever will be equal to 1.

Wikipedia
In mathematics, 0.999… (also denoted or ) is a recurring decimal exactly equal to 1. In other words, the symbols '0.999…' and '1' represent the same real number. Mathematicians have formulated numerous proofs of this identity.

 

[readingstockport]

the quote from wikipedia

So what? 1 equals 1. Anything else does not and if you assume that it does it will introduce rounding errors. Those errors may be neglible such that they in most instances can be ignored but it does not mean they do not exist. The sign = means equality, there other mathematical symbols which mean 'almost equals' or 'approximately equals'.

 

[maffew]

Bollocks. NO mathematician anywhere will EVER accept that 0.99.... recurring is equal to one. They will accept that it is approximately equal to one but in mathematics and physical sciences the term eqaulity means EXACTLY what it says on the tin. EQUALITY. They are EXACTLY equal.

0.999........ is not and never ever will be equal to 1.

whilst I kind of agree with you, .99999999 recurring is accepted as 1 by mathematicians

or
_
1 = 0.999

the hat should be after the last 9 though it keeps moving

 

[fork me]

Bollocks. NO mathematician anywhere will EVER accept that 0.99.... recurring is equal to one. They will accept that it is approximately equal to one but in mathematics and physical sciences the term eqaulity means EXACTLY what it says on the tin. EQUALITY. They are EXACTLY equal.

0.999........ is not and never ever will be equal to 1.

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