[Off-topic] finalhit:
grrr, i refreshed the page, and lost my post..

anyway, starting with the bottom quote:

1) 3/3 = 1. having the same number represented multiple ways is not ridiculous.

2) creating a scenario that real numbers don't exist, then concluding properties of real numbers no longer work doesn't prove anything.

the property of the continuity of real numbers only apply when real numbers exist. your 3=4 argument is moot.

now top quote:

the author isn't saying what you think he's saying

http://en.wikipedia.org/wiki/Hyperreal_number

because it is true that .999...=1 it must also be true that .999=1 in the hypereals.

it's seems you've already yielded (agreeing with that link) that .999...=1 ( at least in the reals), why do you keep arguing? it seems you just want to argue to not have to accept you were wrong?

you accept the premise mentioned in that article, but still hold that you're right, and .999.. != 1. Holding two contradictory statements at the same time is crazy.

would also like to point out the author of that article is not a mathematician. if you read the article being cited by the author, it talks about how to teach why .999... = 1, rather than .999 < 1 in hyperreals.

here's the article cited by the author of that post.

http://arxiv.org/pdf/0811.0164v8.pdf

please read chapters "i told you so" and "coming clean".

your side has time and time again agreed with articles that disproves your point...only because they sound like they agree with you. this is clear demonstration of a confirmation bias. you're not testing your belief if they're correct, you're merely looking for people that may agree with you, regardless of the validity of what they say.

what you feel isn't always right, and in this case, they have been proven to be wrong.

---------- Post added at 11:05 PM ---------- Previous post was at 11:02 PM ----------

no it's not. it's not an approximation. to say it's an approximation is to believe you never reach your destination.

...not having read the thread, you wont' get that reference, but i'm not about to accomodate you for that. please read the thread, this has been discussed.

---------- Post added at 11:08 PM ---------- Previous post was at 11:05 PM ----------

mathematicians didn't just say it...they proved it. big difference.

---------- Post added at 11:11 PM ---------- Previous post was at 11:08 PM ----------

you're being intellectually dishonest. the only remotely meaning argument you've made is that last link you posted (oops, you didn't post it, but you agreed with it), about reals vs hyperreals. with it, you claimed "it can go either way" depending on the number system.

it's not that we can't comprehend the difference between 1 and .9..., it's that there is not difference between them. you have to get over your hangup about having a single value being represented multiple ways. 3/3 = 1. deal with it. i think this is your main problem understanding why .9...=1. you think it's "ridiculous" for 1 value to have multiple representation.

again you've yielded on the reals, just not the hyperreals...which of course is wrong. all statements that are true in the reals are also true in the hyperreals.

so whatever your position is, it's not based on any meaningful mathematical properties. you're just beholden to what you "feel" is right. which of course, is based on the lack of understanding of math.