Poll: Does 0.999.. equal 1 ?

[funguy2121]

Essentially, yes.

1/9 = 0.111..
2/9 = 0.222..
etc
so 9/9 = 0.999..

but 9/9's is a whole, so it is also 1.

Yeah my maths teacher told us this once

Predicated upon a false assumption. Any number divided by itself = 1, including 9/9, which most definitely does not = .999.

A is always A. If someone is subverting the law of identity (that'd be Aristotle, not math), they are lying to you. Nothing in depth about it.

 

[The_root_of_all_evil]

These are several incorrect statements.

Your mathematical skill is matched by your grammar.

I especially enjoy "Only one side is correct" in an equation-based argument.

0.(9) is irrational because it only exists in reference to decimalising a fraction. That means that it is equivalent to 1, because there is no way to represent the numbers tolerance.

Commonly, it's known as "rounding" or "truncating". That's taught in GCSEs.

0.5(ru) is equivalent to 1, 0.5(rd) is equivalent to 0. Neither are equal. You can argue as much as you wish about it, but you'll be arguing about semantics.

 

[gmaverick019_v1legacy]

seriously, there are proofs pouring out everywhere on every level of math, .999 = 1

please, just accept it, due to base 10 laws of math it must be true.

 

[1000000]

I'm actually really surprised that the majority of people are wrong here. I guess I gave the population of this forum too much credit.

Yes, 0.999... = 1

 

[Hashime]

It depends on the confidence you have in your measurement of 0.999.
If you confidence that the value is 0.999 is great enough the number will be 0.999. However if your confidence in the measurement is say 95% there will be a range of acceptable values making it possible for 0.999 to effectively equal 1.
http://en.wikipedia.org/wiki/Confidence_interval

Edit: The OP did not use proper notation writing down that 0.999 was in fact 0.999 repeating.
This changes things.
The lower primate in us still resists, saying: .999~ doesn't really represent a number, then, but a process. To find a number we have to halt the process, at which point the .999~ = 1 thing falls apart. Nonsense.

 

[Nimbus]

In our system of maths, 0.9999.... and 1 are two ways of writing the same number. Simple as.

 

[qeinar]

1/3 = 0.333...
0.333...*3= 0.999...

on a different calculator

1/3 = 0.333...
0.333...*3= 1

Mathematics is flawed

nah it's the calculator. ^^

 

[qeinar]

Essentially, yes.

1/9 = 0.111..
2/9 = 0.222..
etc
so 9/9 = 0.999..

but 9/9's is a whole, so it is also 1.

Yeah my maths teacher told us this once

Predicated upon a false assumption. Any number divided by itself = 1, including 9/9, which most definitely does not = .999.

A is always A. If someone is subverting the law of identity (that'd be Aristotle, not math), they are lying to you. Nothing in depth about it.

Wow gj to your math teacher for teaching you false maths. xD

 

[Rough Sausage]

University student here, studying maths. 0.(9) is exactly equal to one. Look at this way: If you were to take 2 distinct numbers, you could also find a number in between them. Take 0.(9) and 1. Is there a number between them? No. Therefore, they are equal.

 

[Robert632]

My gut keeps screaming "NOOOO!", but then I'm reminded of this, and many other proofs;

x=.9999...
10x=9.9999...
10x-x=9.9999...-.9999...
9x=9
x=1
.9999...=x=1
.9999...=1

And then my brain beats my gut till he admits that it's true.

 

[zehydra]

No, 0.9999999... = 0.999999999...

For the same reason that 0.33333333 does not equal 0.3.

 

[minus_273c]

It depends on the application and the required accuracy.

So yes, 0.999 = 1.0.

Except when it doesn't.

 

[Jack Skelhon]

Mathematically, it cannot under any circumstances. 0.999 cannot be correctly expressed as a fraction unless it's 999 over 1000. It is NOT equal to 9/10, and neither is it technically equal to a third; three thirds equal 1, and therefore it is not a third.

Remember; there is NO decimal version of a third because it's a hypothetical number that can only be expressed in a fraction format. One is not divisible into three except in theory because it relies on infinity, which doesn't technically exist; hence the use of the fraction.

Decimally and fractionally therefore 0.999 is exactly 0.001 and/or 1/1000 UNDER one.

It cannot, under any circumstances be expressed as 1. Anyone trying to do so is wrong.

There is no construed logic, argument or otherwise. Maths is pure logic, and there is zero interpretation. 0.999 cannot equal 1. This statement is true. That is inarguable. That is pure fact. This is maths, and you are wrong if you think vice-versa.

Let me put it this way.



If 0.999 were 1, why isn't it 1?

 

[Halceon]

The search box weeps, it weeps tears of abject horror.

Anyway, do your intuition pumps of simple multiplication still work here, in binary?

0001/1001 = 0,000111(000111)
0011/1001 = 0,01(01)
1001/1001 = ?

What about base-3, where the same expressions go

1/100=0,01
10/100=0,1
100/100=?

 

[Celtic_Kerr]

x=.9999...
10x=9.9999...
10x-x=9.9999...-.9999...
9x=9
x=1
.9999...=x=1
.9999...=1

This is such a flawed algebraic expression though. albegra is about normally using the most direct method. If you already know X then it should be

x=0.9999
10X=9.9999
10(0.9999)=9.9999
9.999=9.999

Manipulating math to technical possibilities is technically flawed, but correct. There is still an infinitesimally small difference

 

[Canadamus Prime]

No, but it is so close to 1 that the you could just count it as 1.

 

[MrJKapowey]

0.999 doesn't equal one

0.999[small]r[/small] technically equaly one (r = recurring)

 

[Lord Beautiful]

My keyboard has a face-shaped crater from seeing all the people who voted "no."

 

[Rough Sausage]

0.999 doesn't equal one

0.999[small]r[/small] technically equaly one (r = recurring)

I think by the ellipsis he means 0.999 recurring. Just sayin'.

 

[Alfador_VII]

For practical purposes, and especially if there's any sort of rounding involved, they come out the same. If you do any sort of calculations on a computer or whatever, you'll probably come to the conclusion that they're equal.

It doesn't matter how many decimal places you go to, 0.999... is still slightly less than 1

HOWEVER, mathematically, definitely not, they're extremely close together but not identical. It comes down to proofs, and definitions. The two numbers are not the same. Saying that they are would be logically the same as stating that 1=2.