Notice!: Before you close this thread becuase you don’t have a huge understanding of mathematics, read on friends, fore you will not need to understand math for the purposes of this.

I browse some other forums, though don’t spend nearly as much time reading them, as I do reading this one. Recently though, I found a gem in the “rough” that is the internet, though “rough” might not be the right term. Any website that isn’t pornographic is probobly as rare as a diamond, but I digress. The post I did find, was one in relation to mathematics, and was simply a mathematical proof for a relativily simple equation, that (supposedly, according to these forums) Philosophers and Mathematicians have fought over for quite some time.

For the purposes of this post, let the number “0.999…” be equal to “0.999(repeating)” becuase the forums don’t allow me to make the number with the repeating bar over the top.

The following proofs are to show that the number 0.999… is equal to the number 1. ( 0.999… = 1 )

The conversation got to be very philosophical. I was just curious what everyones thoughts and opinions are on this topic. I will let you all know how I feel, as this topic goes on. Mostly becuase I would like to see how you all relate this math problem to philosophy, and such, without my input.

please do not turn this into an argument over weather these equations are correct or not, they are mathematically sound. The question is, how do you feel how correct they are, based philosophy, or what sort of effect they have on philosophy, etc. Not weather they are correct, becuase mathematically .999… does infact equal 1.

I confess I’m not much of a mathmatician, so this keep this bias in mind throughout this post.

With the exception of logics, I find that philosophy and mathmatics do not mix all that well. This is because of their objectives. Philosophy has an inherent interest with why, while maths and sciences are much more interested in how.

However, I do not believe that .999 (infinite) can ever be said to equal 1. Not ontologically anyways. Aesthetically, they may function the same.

Another question I’d be curious about is: could you have a triangle if one angle is 179.999 (inf.) degrees? In theory, it should be possible, but in practice, I’d wager not. I believe this is on par with what you were wondering.

It depends on the view of mathematics being a purely abstract realm or a representation of the physical.

If 0.999… is a physical representation, say a length, energy, momentum etc. it is then a question of whether there exists some fundamental, irreducible quantity in the physical world. If this is the case, then physical quantities will be discrete and 0.999… will always be one of these quantities less than 1.

In the case of mathematics taken as a purely abstract, non-extended form, then this may rely on whether the abstraction of the concept of infinity is valid, or knowable in a finite mind. I think we can have a concept of infinity, but whether this concept can be applied in mathematical operations to attain some a priori “truth” is another question.

If you want math and philosophy combination, try intermediate logic.
Problems that comes from that, will drive one to the death. Like the founders for that subject.

My in-a-nutshell reply is that 0.9-recurring is equivalent to 1 because it is in fact the fraction 9/9 (0.8-recurring = 8/9, etc). Plus, the difference between 0.9-r and 1 is 1/infinity, which equals zero too.

Me and my mathematically-inclined brother have argued this one with my mathematically-uninclined other brother