i disproved that by showing how one limits oneself by using division, and i did use math like 20 posts ago, nn u to post again

The square root of negative seven is not a real number either, but that doesn't mean you can't use it in mathematical equations. By doing simple addition, subtraction, multiplication and division, you learn that 0.999... is 0.000... 1 away from infinity and 0.999... + 0.333... = 1.333... 2 but if you kept reading you would see that I wrote that anything after an infinite series does not exist, therefore 0.000... 1 is exactly equal to 0 and is denoted by 0 because the 1 after the infinite series does not affect the answer or provide any error whatsoever.
Please read the whole thing before you try to argue, thanks.

I did read the whole thing. You have the correct end result (that there in fact is not a 2 at the end of 1.333...2 for example). But your explanations are wrong. Stuff isn't being ignored. Again, I read your entire post, and I addressed everything that was in fact wrong.

You and I are talking about different "real" numbers. When I say "real number", I'm talking about an element of R. I'm not saying that a number that's not "real" doesn't exist. You're right about the square root of a negative being non-real; this doesn't mean it doesn't exist. (I did NOT say anything about that). It very much exists - as a complex number, which is not real (that is, it does not belong to R. For example, sqrt(-3) is not in R; it is a complex number belonging to the set of complex numbers, C).

So again, .000...1 is NOT a real number. 0.999... is NOT 0.000...1 away from 1. This is IMPOSSIBLE because 0.000...1 is not a real number. 0.000...1 is not exactly equal to 0 because 0.000...1 is NOT a real number.

If you're interested in proofs of the particular property of R that necessitate that no nontrivial infinitesimals exist, check out http://en.wikipedia.org/wiki/Archimedean_property

No need for the attitude. I'd just rather have the people who know that .999... = 1 know more about it

This post was edited by chone on Jul 9 2010 01:17am

Real numbers are represented by "R" and rational numbers are represented by "Q" right? I understand what you're saying with the 0.000... 1 being equal to 0 because 0.000... 1 does not exist, but I couldn't really explain it very well because when someone who knows very little about the concept of infinity comes along and says that 0.999... + 0.333... is not equal to 1.333... because it has to have a 2 in it somewhere, I usually just resort to that theory to say that the 2 is "ignored" because it is after an infinite series. Then the person tells me that you cannot have something after an infinite series and that you also cannot ignore numbers, but if I tell them that it is 1.333... then they ask me how did I end up with all 3's and no 2 at the end of it?
I know what you're saying and I'm not trying to be rude or anything, it's just I don't know how to explain it any other way to people who do not understand this sort of stuff.
But thanks for the wikipedia info

Yep. More specifically, R is the set of reals, and Q is the set of rationals (which is a subset of R). Z is integers, C is complex, N for naturals.


Well, what I'm really getting at here is that saying "0.000...1 is equal to 0" actually literally makes no sense. You just can't compare these numbers.


The better way to do this is to tell them that there *can't* be a 2 "after" the infinite numbers (because that wouldn't be a real number), and then to ask them something like:
"If 1 and 0.999... are not equal, then clearly there is something between them. Give me any number between them"
The only thing they can think of is something that's not a real number (like 0.000...1). If they can understand that there can't be any real numbers between them, then, well, they must be equal.


This is a difficult question to answer, and the answer is kinda tricky. It really just comes down to how we cannot adequately write down an infinite number of threes. It's not just our normal number system, either. For example, in binary .111... equals 1. Same shit, different smell.

sigh... i remember posting the 3rd post in the original post of this shit, and now its all the pay up to 100 pages with 5600 views and 1000 replies...

simple answer to this is ...

1 and .99999.. doesnt equal the same because of no mathmatical meaning... let put it into context shall we?

a kid is walking accross the street... he is 10 feet away from the sidewalk when a bus passes the street...

now lets tell a second story

a kid was killed in a tragic automobile accident today when a bus hit him while he was attempting to cross the street (he was just a little bit short of that 10 feet...)


End

The second answer to this is

the reason you cant calculate a equation for infinite is because it doesnt exist

there is nothing in the knows universe that equals infinite, thus, making number and equations on mathematician part was ignorant (there is no proof space continues forever so dont use this as a example)

This post was edited by ]GS[ Controller on Jul 9 2010 04:37am

ugh..... please stop relating everything to real life terms. we understand 99 cents isnt equal to 100 cents and when something is 99% ____-free it doesn't mean 100% ____=free

WE are simply just stating the mathematical theorem that an infinitely repeating decimal .9999999.... will continue forever. it IS true. .999...=1 and I'm sorry if you seem to disagree, but mathematicians who do this for a living have proved this theorem multiple ways

There are infinity particles in any object (eg. an atom).
For example, what makes up an atom?
Protons, neutrons, electrons.
What makes up them?
Strings.
What makes up the strings?
Not currently known.
But there is no limit to how small things can get and whenever you say "nothing is smaller than ..." then you are wrong because there are always smaller things that make that thing up.
Also, just because you cannot name something that is infinite, doesn't mean that we should wipe it away completely.
There is nothing that is equal to the square root of a negative number in reality, but we still study complex numbers.
Maths is about finding patterns and realising things. Even if that thing does not affect you directly, you will learn from your ability to spot different patterns and make calculations.



this

edit: Post #999

This post was edited by Hammer_Hdin on Jul 9 2010 06:07am

Post #1000