## Does 0.9999(repeating) = 1?

Yes 705 54.95%
No 578 45.05%
Voters: 1283. You may not vote on this poll

### Does 0.9999(repeating) = 1?

First Riot Post

Grandpappy

Senior Member

Quote:
Originally Posted by Ryster
This is a very highly debated concept, even among mathematicians today. It can be proven for both sides that it is true. This is basically which ever one you think it is true. You are never going to use this concept in the real world, so it doesn't matter.

I myself think it equals both, or at least can equal both based on the need. But yea, there will always be people on both sides.
I have not seen a counter proof. Can you post one?

Limited Reactant

Senior Member

Quote:
Originally Posted by Ethri
I'm confused.

If x=0.999...
10x= 10 (0.999...) So far so good.
9x= [10(0.999...)] - 0.999
How does this step work? Even if you could subtract 0.999 from a number being multiplied, wouldn't it be 9.111... on the other side. Forgive me I haven't done math in a while.
9x= [10(0.999...)] - 0.999 = 9.999... - 0.999.... = 9

Ur little sister

Senior Member

There are several proofs of this. The main confusion comes from the idea that the difference between 0.99... and 1 is infinitisimal, and a poor understanding of what exactly that means. It's a tougher question than it appears to be, and I remember in my first bachelor year (I study astrophysics. Our first year is largely shared with mathematics students), there was some discussion about it.

Anyway, a key property of real numbers is that if you take 2 different real numbers (say a and b, with a =/= b), there always exists at least 1 real number that is in between them. I believe this is called the density property. It also applies to rational numbers. This property disproves the existance of any real number that would be "the largest number that is smaller than 1".

So we're left with this: either 0.99... isn't a real number, or it is, in which case it can't be "the number closest to 1". Now we know that 0.33... is a real number, it's how we choose to write 1/3. So assuming that that notation is consistent, then 0.99... is a real number, and it's just how we choose to write 1/1. In other words, numbers don't have 1 unique way to be written.

MrGrimm999

The Council

Ok try this out.

3/3 = 1

1/3 + 1/3 + 1/3 = 1 right?

1/3 = .333333 repeating

.33333 repeating X 3 = .999999 repeating

Since 3/3 = 1 and 1/3 X 3 = .999999 repeating and 3/3 = 1

.9999999 repeating = 1

Chaldron

Senior Member

Quote:
Originally Posted by I*******I
mathemathically is equal

in the real life not

for example: If u have 3 cars and one of these is cutted by half, u have in fact 2.5 cars, not 3

So math and numbers are abtract, u can aproximate everything with maths but you can&acute;t aproximate in real life.
Its not rounding

Kazral

Senior Member

Quote:
Originally Posted by leetnanas
Again, you're looking at it from a math perspective. (I have a feeling GD's logic wont be able to follow what I'm about to say... but here goes.)

Lets say we looked at it from an Artistic stand point.

If someone Painted a 1 on a canvas

And someone Painted a .9999999 on a canvas

And this was prehistoric times and no one understood math... would the painting be the same?

Of course it wouldn't. It would be different. One would show a 1, one would show a .99999

Open your minds and think outside the box.
Yes, the literal strings are different. That's like saying because I have a name and a nickname, I am a different person based on which name I am being called at the time. The numbers that we write down are just representations of abstract ideas. The "number one" isn't a physical thing you can touch or see, but representations are easy to find.

Lénekton Bot

Senior Member

1/9 = 0.111...
9* 1/9 = 9 * 0.111...
1 = 0.999...

Imogen Poots

Senior Member

Quote:
Originally Posted by Insentience
Me and a friend were having a debate whether or not 0.999... (for those who are confused the 9 is repeating.). I'm saying it does = 1, but he says it doesn't. Though I think I may be right, but there is always the benefit of doubt, and I am open to hearing what others have to say.

So if 0.999... does equal 1, then explain how it equals 1.

but if 0.999... doesn't equal 1, then explain how it doesn't equal 1.

This has been bugging me for awhile.
Like everything in mathematics, the truth of a statement is always a consequence of rules and definitions. Mathematical rules and definitions don't necessarily have to translate into something that makes physical sense.

This seeming contradiction to common sense has its roots in the definition of "infinite." Infinity is not a very large number. It is infinity. Infinitely small is not a very small number, it's 0, by definition.

1 minus an infinitely small number is the same thing as 1 minus 0, because an infinitely small number is 0 by definition. Therefore 0.999... is 1 by definition. Get it?

FoxMindedGuy

Senior Member

No matter how many 9s you add after a decimal, it will always be LESS THAN 1.

However, if you use the limit theory and there is an asymptotic function that goes nearer and nearer to 1 but never touches it, then you can say that as x = infinity, y would equal 1. Keep in mind, we say that for simplicity and in reality there would be no real value (infinity is NOT a real number) that could make said function to reach 1.