Your favourite source Wikipedia also lists multiple uses of the infinite set of real numbers.

I just ran a simple regression from the data, didn't even included deviations and such so there's isn't much to look at unless you check the datapoints thoroughly (basically redoing the whole stuff). It's just a small calculation to get a first impression :)

We are getting really off track in this topic.
0.999... =1, QED.

ah... yeah great circular logic gobble. real numbers include any possible number on the number line. genius. if you're trying to say it includes both rational and irrational numbers, i already said it should.

it does.
no-one ever said it doesn't.

the point i'm making is that you have a number like pi, that is not rational. so you can call it irrational. and there are numbers like 1/3 that are rational. but then some people extended this by saying pi is actually an infinite set of digits (after the decimal place) and we'll just imagine all possible combinations of numbers with infinite digits after the decimal and call that the real line. that's what i don't like. this abstraction.

so basically your problem with mathS is your inability to comprehend infinity.

are you another believer in second-order infinity yellowjacket?

but the definition of real numbers is fundamental to all high-level mathematics. The world runs on real numbers not to mention complex numbers, higher-order vectors, etc.
To deny that the real number system should exist as it is defined would mean overturning the fact that you can pay by credit card, that your local power station would work, that your bus or car would run, etc. Everything relies on the real system.

Also, real numbers are in fact belonging to the second order infinity, as opposed to rational numbers/integers that belong to the first-order.
Learn your mathS first.

that is retardedly false, i don't even know where to begin. nothing is based on this real number continuum.

@bolshoi, your argument boils down to your inability to think abstractly? Good luck to you.
@Gobbledydook, technical detail: everything relies on the complex number system, not the real.

I don't even know what a second order infinity is. But unlike you, bolshoi, I'll cheerfully admit my ignorance.

@bol

I'm sorry if I missed your answer, but this thread is moving too quickly for me to keep up.

What is your background? How old are you? What are/will/have you studyinged?

hahahaha, oh ok, so you've refined your definition, now second-order infinity is uncountable. that's good. at least now i know what you mean when you mention it.

lol@bolshoi:
good luck. all the physical models and such rely on the real number set to function. Sure, measurements are not accurate to infinite digits but the model that is used to fit the measurements are all done in terms of functions over R and/or C.

bolshoi, not sure if you are trolling or what.
You mention countability in mathematics, a no doubt university-level (and not intro-level) concept, and yet you can't grasp the necessity of the real system, which is taught in high school, and is also a huge concept in university maths.

oh you didn't miss my answer, i just didn't give it cause i don't really feel like it.

lol it's part of what bolshoi calls proof. See earlier page in this thread.

@bol

It's a shame because if you were, say, a HS student, we could explain why your ideas break down at a more advanced level. If you were, say, a communication major, we could all just give up.

lol abge, always the cool and collected one. He's refused repeatedly to tell us where he's at. I'd say he's a troll but he's putting too much effort into this. Hence my aspergers theory earlier

as far as i'm concerned none of you have proved anything here. so i'm not sure where you see my ideas breaking down. if i had someone prove me wrong i might feel bad about it, but this argument is just like the one i was having about global warming. people are all convinced they have proven me wrong... but i just don't see it. maybe someday i will be smart enough to see how you all did cleverly prove me wrong. but i'm sorry to say that day has yet to arrive.

Me and YJ proved that you suck at debating.

This is completely different.
Climate science is about observing real-life and then forming hypothesis. It is possible for scientists to be wrong about it.
Mathematics is an entirely artificial construct. It is an axiomatic system where theories are based upon each other, down to the most basic level. Mathematical principles and theories have been defined so that they are useful for computation, not because they reflect some real-life data. Since the real continuum is useful for understanding mathematics and arriving at conclusions, it is defined as such. It is abstract by definition, just as mathematics is.
Whether you can understand mathematics is irrelevant to whether it is valid. Real number theory is based on a set of axioms and theories that are mathematically and logically sound, and if you are interested in doing mathematics then you must accept that it is correct.

not really. you can come up with something in mathematics that has no basis in reality, like an oracle, so that's fine for messing around. but when people use the term "real" to describe numbers they see in the reality, and think of it as some number with infinite number of digits after the decimal, they are maybe missing something. you don't have people going around calling computers oracles. like "oh say you have a computing device in O, the set of oracles", it's retarded. but the real number line is somehow not supposed to be.

Help.
So now you are being semantic? Would it please you better if it was called the Zimmerman Numbers instead of real numbers?

i wasn't trying to be semantic. maybe i'm just getting tired so i'm not making sense. i just think it's a bit of a scam to think the set of reals is uncountable, that's all i'm saying. if they are imagining an uncountable set, than they are not imagining reality. people usually think the real line does exist in reality though, it is taught to.

@bol

"as far as i'm concerned none of you have proved anything here."

I've seen a number of proofs of various rigor for 0.9...=1. You found problems with all of them?

The problem is that you are asking questions about proofs. You're talking about feelings, like "I don't like real numbers" or "this is too abstract". What are we supposed to prove? That you do like real numbers?

IMAGINARY NUMBERS!!! I love those. The square root of -1 is an imaginary number.