The Saga Continues

(note:  this post has been closed to comments;  comments about it on other pages will be deleted!)

UPDATE, WITH REFUTATIONS!

First of all, thanks very much to the Goodmath/Badmath blog for linking to my .9999...=1 post, and thanks to all the people who posted on my blog, too.

There were more demonstrations in the comments of how .99999...=1, and I am sure there are more.  The original post was never intended to cover them all, of course.

But the original troll (removed by request) made the following comment that just has to be addressed (I only feel like it's okay to post it because he posted in the comments.  I won't use e-mailed text without permission):

I was going to post a rebuttal with complete proof from 2(two) ASU mathematicians (who both agree with me), but upon review of all your posts, I came to the ultimate conclusion that you don't need proof. You will go to your grave believing with the core of your being that .9999999... does, in your mind, equal 1. However wrong I, or anyone else may think you are will not matter. Trying to convince you otherwise is like trying to convince an atheist that God exists.

So I am sending him (his e-mail address suggests his gender) the following e-mail, noting to him that it is also posted here:

You seem to be misunderstanding the nature of mathematical proof and belief.  The belief that .9999...=1 is not in any sense a religious belief as you imply.  If I ever see a mathematically sound proof that .9999... does not equal 1, I will humbly admit my error, and become a vocal proponent of that proof.  I repeat what I said in an earlier comment:  if you send me a proof that is verifiably (and I will check it out) by a mathematician at an accredited university (ASU is an excellent choice) that uses the standard real number system, I will post it on my blog with sincerest apologies to you, and then I will explain it on the blog to the best of my ability, including the reasons my previous proof was incorrect.  Until then, I will continue to side with the overwhelming majority (100%, as far as I know) of the mathematical professional community who agree with me.

The challenge, of course, is open to anyone.  This space is available for such a proof, if any should appear.  I'll update again if anything turns up, but I'm still not gonna hold my breath.

Comments

[sulliwan]

Last sentence should be:

Since it has been shown there exists a number that is greater than 0.(9) but less than 1, 0.(9) != 1.

[sulliwan]

Wow, this comment system is shit.

Last sentence should be:

Since it has been shown there exists a number that is less than 1, but greater than 0.(9), 0.(9) != 1.

[Patrick]

Doing this as more of a thought experiment if you had .9 and 9 repeating infinitely it would approach and equal 1. In actual practice you can never actually reach infinity because well it is the nature of infinity.

I think that is sort of the bump that confuses a lot of people. The people who say it does not equal 1 seem to be in the mind frame that infinity will just create an infinitely small difference that gets smaller and smaller and small for infinity, but still leaving a difference.

The side that says they equal each other seem to look at it from more of a hypothetical where infinity is reached, even if you can't really ever get to infinity.

The thing is that these sort of hypothetical assumptions are done all the time in various fields and they usually seem to be accepted without much question. The exception to this seems to be with infinitely repeating digits.

I mean, if you can accept absolutely no friction in a thought experiment, why not accept infinity being reached? Or you could just take the easy route and use significant digits.