Better stop having opinions then. There is nothing similar between dividing by zero and applying simple math correctly.

@Mint

Your opinion is not only irrelevant, but it is wrong.

" then in normal terms "

What does this even mean? The *vast* majority of math can't be understood or expressed in "normal terms".

Explain to me what the normal equivalent of the Schrodinger Equation on an infinite (yes, infinite) Hilbert space is. There isn't one. Does that mean it doesn't exist or that it can't be used to tell us real information about the real world?

That is an incorrect view of recurring decimals.

1. Recurring decimals are by definition rational numbers. They can be expressed as fractions. They are decimal representations of fractions, that cannot be expressed with a finite number of decimal places.
2. Recurring decimals are converted to fractions by doing that multiply by a constant then subtracting trick, for example if 1/x = 0.166..., then consider 10/x = 1.666..., 10/x - 1/x = 1.5. (There are infinite 6's that cancel each other out). Then x = 1/6.

There is nothing inaccurate about 0.99999, it is simply a representation of the fraction that is 3/3, or 1.

Now, I will say, you bring up a good point: You can make a proof that arrives at an illogical conclusion if you take liberties in the middle.

However, I can directly point out the error in your 1=2 proof. You can't divide by 0.

Now, where is the error in the 0.9...=1 proofs that have been laid out.

Maybe they cannot get to grips with this

if you had x "9"s in the 0.9999.., then if you multiplied by 10, then there should still be x "9"s, just as 9999 x 10 = 99990, there is no 9 at the end. Therefore when you subtracted, the last 9 in the 0.999... could not be cancelled out.

The problem with this thinking is that you cannot actually cancel out infinity. Infinity is not a concrete number where you can perform arithmetic. This also brings up a problem though: how do you say the 9s in the 9.999... and the 0.999... cancel out completely if you cannot compare infinities? The proof given on the first page is not a formal proof.

Time to bring out the heavy artillery...the Formal Proof anyone?

abge is absolutely correct here.
It's rather irritating that people think their subjective opinions always matter. Mathematics is an axiomatic system that builds up logically; it is internally consistent and as we use it for just about everything that we do in this technological age, it is externally consistent as well. It is not a matter of personal preference regarding any one idea within the system.
"Normal terms?" That sounds like if the idea isn't expressed so that you personally can understand it or that you are inclined to agree to it, the the idea itself is up for debate.

Also the reason climate change skeptics and creationists exist.

Also, can anyone provide a formal proof that does not require subtracting numbers with infinite decimal places?

There's no need for a formal proof. Someone who can't understand a rationalization aimed at elementary school children will not be persuaded by a formal proof either.

This thread doesn't need 0.9999999... more post.

@ulytau:
Nevertheless a formal proof must exist, and though they will not have the mental capacity to understand it, I would like to see how it is formally done.

@gobbledydook,
If people who have problems with the proof(s) given on the first page, then why do you think more sophisticated or "formal" proofs will convince them? If they think their opinions matter on the basic rules/definitions of mathematics or logic, then why would they "accept" the concepts of limits, of abstract algebra, of delta and sigma? Some ideas, such as gravity, can be explained or "watered down" for the general public. Almost every educated person understands what gravity is (I hope), but when you start talking about general relativity and the space-time continuum, the faux understanding of "gravity" melts away. The fact of the matter is that most of us are not capable to really understanding how axiomatic systems work because we do not have "real life experience" equivalents for them and most of us understand what we see and deal with on a regular basis.

For a very math-oriented example, the principle of mathematical induction is one that eludes the vast majority of people including doctorates of other fields and many undergraduate math majors. Let's go with just the weak induction:
You are trying to prove that P(n) is always true for n>=1 (n is an integer). Here's what you need:
A. Show P(1) to be true.
B. Assume P(k) to be true and show P(k+1) has to be true.
If you have both A and B, then P(n) is true for all n>=1.

@zultar, i'm sure i did induction in school (not college) at around 16...

@orathaic, math induction is taught at various levels, and some high schools do teach it (not most unfortunately). My point is that it is still an idea that is fully hard to grasp even for well-educated people.

ok, i take your point, i guess the point of my post was that i had assumed everyone was taught this, and that everyone got the concept (even if they failed to successfully prove something by induction) - your simple explanation of induction seems pretty easy to grasp, imho

Yeah, when you actually start asking probing questions, most people can't really explain why A and B would necessitate in all n's being true. It's actually easier to teach people how to use induction to prove something than it is for them to truly understand why it works and its implications.

http://blog.stackoverflow.com/wp-content/uploads/then-a-miracle-occurs-cartoon.png

I know my opinion is rather insignificant, and I know my proof is easily proven wrong as you can't divide by 0. I'm no whizz at maths, I just like to see other peoples opinions and improve my understanding by learning from others. If my argument is overall largely irrelevant I will learn from it. I try to listen to criticism. which is why I don't like trolls even though I sometimes troll myself..
This is probably the last I will be posting on this topic as I believe my knowledge of maths is to insignificant to further contribute to this topic. However I am likely to still keep reading so keep it interesting :)

OK really, I'm not the type to boss people around or give orders, but I absolutely forbid any further posting on this topic. For those on the wrong side of it, I forbid further posting on ANY topic.

if I see any more stupidity whatsoever on this matter I swear to God I will teach myself to hack, rewrite myself as a mod, ban your account, find out Draugnar's home address, torch his house (why not?), then cancel webdip's server subscription and spend the change on hookers and blow.

I hope i make myself clear.

Your pal,

YJ

So, I've been thinking a lot about this, and I've now decided that my opinion is that .999...=infinity because there are so many nines and when you add them all together it makes sense that they would equal infinity. I'm leaving my newly formed opinion open to criticism and debate.

@Gobbledydook
"Also the reason climate change skeptics and creationists exist."
ok, we're all having fun (i hope) with this 0.99... debate. but don't bring your co2 garbage into this. the theory that co2 drives world temperature is completely unproven.

Sorry YJ, it looks like I didn't even need to continue the stupidity myself. Enjoy the hookers and blow, and maybe consider sharing with the rest of us.

Bolshoi, that point had been dropped, but you just *had* to bring it back up. Look at the way climate models have accurately predicted everything (on a large scale, obviously there are short term discrepancies because there are too many variables to model everything exactly), and then look at the fact that the only scientists that dispute climate change are scientists that have absolutely nothing to do with the field and who almost always have ulterior political motives. You can't claim to know more about this then thousands of really intelligent scientists while claiming that opinions have a place in mathematics.

i didn't actually read every post, so if the point was dropped, then it's my mistake. yeah those models were fantastic, particularly the original ipcc one that generated the exact same hockey stick independent of what data is put into it, even random garbage.

I'm going to paraphrase your last post as "the first one sucked, therefore they all suck." Do you have any idea how the practiced medicine hundreds of years ago? All science starts off incredibly basic and often very wrong in its assumptions, over time the field will advance, and eventually they have evidence supporting their theories that is conclusive beyond any reasonable doubt. The current climate models are surprisingly accurate, and the only thing in question is how much change is actually happening.

except recent nasa satellite data has disproven underlying assumptions of the later models.

Source?

i don't know, here's a source from forbes, a well-established leader in the scientific field. but if you care that much, i'm sure you will be able to find a more scientific source yourself.
http://www.forbes.com/sites/jamestaylor/2011/07/27/new-nasa-data-blow-gaping-hold-in-global-warming-alarmism/

Heh, "forbes, a well-established leader in the scientific field," that's a good one.

Before addressing the findings themselves, I'll point out that that article is INCREDIBLY biased. Check out where the author works, http://heartland.org/

Now, I'm not an expert on the subject, so I can only repeat what's been said, much as you can, but the paper your article references seems to come up less than adequate when subjected to proper scientific review. http://www.bbc.co.uk/news/science-environment-14768574

the fact that he was forced out for doing independent research, if anything, is evidence that there is bs going on. when scientists are afraid to do independent research because of serious repercussions, that will obviously skew results.

in any event the data is still there. so it doesn't matter what happened to this guy who reported on it.