Poll: Does 0.999.. equal 1 ?

[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.

 

[mattsipple4000]

if 0.999(r) = 1
then is 0.888(r) = 0.9 ??
does 1.999(r) = 2

 

[Jack Skelhon]

What makes me laugh is people stating "durr don't be stoopid, it equals one"

0.999r or 0.999 isn't one. It just isn't. To think it is is like being an atom away from being within an area; you're still not actually there, regardless of how infinitely small the distance.

The moment algebra, sums or rounding become involved you've changed the fundamental properties of the number and it's no longer 0.999; end of story. You've changed it, and therefore construed it.

The number 0.999 is not one.



Equal is not the definition of a rounded number.

 

[TheEvilCheese]

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, the are equal.

I like this description of it, easy to understand.

OT: Yes, for a multitude of logical and mathematically provable reasons stated in this thred already. I am surprised so many said no.

 

[Atmos Duality]

If I could rationally express 1/3rd as non-repeating decimal (in Base10), this question wouldn't even exist.

Any repeating decimal is representative of decimal's inability to rationally express an infinite repeating division operation in Base10 (we keep dividing to attain a precise answer, but the logic loops infinitely).

As soon as you stop thinking purely in Base10, the logic works just fine. .99 (repeating) is simply the addition of 3 units of (precisely) 1/3rd.

 

[TheEvilCheese]

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.

1 Isn't 2 you say? Challenge accepted

a = b (initial supposition)
ab = b^2 (multiply both sides by b)
ab-a^2 = b^2-a^2 (subtract a^2 from both sides)
a(b-a) = b^2-a^2 (factor out a from the left side using distributive property)
a(b-a) = (b-a)(b+a) (factor the right side using difference of squares)
a = b+a (cancel both b-a terms )
a = a+a (substitute a for b, legal since a=b)
a = 2a (simplify)
1 = 2 (divide both sides by a)

[sub]Yeah, I know why this isn't true, but I still like the idea [/sub]

 

[Halceon]

If I could rationally express 1/3rd as non-repeating decimal (in Base10), this question wouldn't even exist.

Any repeating decimal is representative of decimal's inability to rationally express an infinite repeating division operation in Base10 (we keep dividing to attain a precise answer, but the logic loops infinitely).

As soon as you stop thinking purely in Base10, the logic works just fine. .99 (repeating) is simply the addition of 3 units of (precisely) 1/3rd.

A swing and a miss. (Or have I misunderstood your statement?)

Try expressing 1/3, 2/3 and 3/3 in base3 (it consists of 0, 1 and 2).

Spoiler

Hint: it is 0,1 0,2 and 1, respectively.

 

[Sebobii]

How many mathematicians does it take to screw in a lightbulb?
0.999999....
(Thank you wiki for making my day)

 

[mps4li3n]

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

The problem is that it's one of those things that seems really obvious whilst you're constantly being reminded of it at school, but is easily forgotten after a decade in the real world.

In the real world it's useless knowledge, easily forgotten, because you'll never encounter an infinitely repeating number.

Actually i blame school for not explaining what math represents better.


Think of it this way, you have 1 apple and 0.99999... apple... if you put them together you have 1.99999.... apples.

Now if you eat the apples and someone else eats 2 apples you will never actually get to the point where you have eaten less apple because it will take an infinite amount of time to get to it... thus there's no real world difference between the apples you and the other person ate.

And this actually works better with you having 0.9999... and the other guy 1 apple... or you eating 1 apple vs 0.9999... apples. You would never be able to get to the difference in time that should exist {assuming the apples are exactly the same besides the 0.(0)1 difference which never comes into play}.

Don't ask me how you'd finish eating the 0.(9) apple.


This is why i distrust math actually... it makes perfect sense... but not really... it's like fucking magic.