[quote=Lucian]
Hah, was this spurred because of that thread I started about the electron? On that subject, by the way, I really only meant what I said in the most rudimentary way. We've observed it's effects obviously, but not it and, in fact, it could be infinitesimally too small to ever observe. I wasn't saying it didn't exist, merely remarking on how it's impossible to see it.
[/quote]

It was, yes. I've had the idea for a while, but your thread reminded me of it. And I know that you meant we haven't visibly seen it - I was just pointing out that visibly seeing it is, in the scheme of things, a very arbitrary way of "observing" something, and that detecting, measuring, observing other properties is exactly the same thing.

[quote=K-97]
Can anyone explain why 1 + 2 + 3 + 4 .... and so on to infinity = -1/12?
[/quote]

Numberphile did an [url=http://m.youtube.com/watch?v=w-I6XTVZXww]excellent video[/url] demonstrating this, far better than I ever could. As for [I]why [/I], the answer will likely lie again in the nature of infinity. I'll get back to you on this one!

[quote=mdk]
Next I'll need someone to explain to me the mathematical difference between reading 1/3 of a post, and reading the full value...... lol. I clearly skipped this part.
[/quote]

It is a ridiculously dense wall of text, I don't blame you for missing a part.... I might go back and restructure some of it, thinking of it.

[quote=Jorick]
But the easiest way to approach it is with some simple fractions. Start with 1 = 1, split one side into thirds, then turn them into decimals.1 = 11 = (1/3) + (1/3) + (1/3)1 = 0.3333... + 0.3333... + 0.3333...1 = 0.9999...Even a middle school kid can understand it with this explanation, no wall of text or even knowledge of algebra needed.
[/quote]

But it does absolutely nothing to explain [I]why[/I]. 

[quote=TheMadAsshatter]
Given that you can make loopholes like these in math, is it possible that math is complete bullshit and the smart guys are wrong? If not, is it not true that math is flawed?
[/quote]

It isn't a loophole. That implies this is like some sort of accidental glitch in the system, than can be taken advantage of to prove untruths or some such. It isn't - it is factually, demonstrably true as per our definition of numbers. Saying that this is a loophole is like saying 1+1=2 is a loophole. 2 is defined by the fact that it is equal to 1+1. Similarly, the way we construct the real numbers, or "how we define numbers", means we have the same definition for both 0.999... and 1, and so they are equal.
Can mathematics be flawed? I don't think so, but it's more a philosophical question - mathematical philosophy, that is. Some believe numbers and relationships in maths already exist and are "discovered", others that they are all "created" by the person who first utilises them. I can go more into mathematical philosophy if you want, just ask. ^_^
What I feel [I]can [/I]be flawed is, say, a number system. See, the way we think of numbers on a daily basis is pretty loose and undefined - as I noted in the original post, most people have never had what a real number is formally defined for them. If you took how we think of numbers on a daily basis and codified it, made a number system out of it, there'd probably be tonnes of flaws and issues. In the study of mathematics, what things [I]are [/I]has to be rigidly defined by rules and axioms of the system you're using, whether that be a number system or a co-ordinate system or whatever. We don't bother with that most of through time though, which can lead to flaws. Maths isn't broken - in my opinion, it sort of can't be, not in itself - but the systems we use can be, though mathematicians are careful to define and prove things, and never just "assume", to avoid that.
Brief note: everything above is purely my own opinion, I haven't done any research for this answer as I'm on my phone. If I read something when I look it up later that contradicts me, I'll correct myself.