bolshoi's commentary is the mathematical equivalent of guro pornography.

I can't stop reading despite myself.

" i am allowing for certain irrational numbers for the sake that you all seem to like them. but for the real world, you need to express those as a rational in order to perform any computation. so really, for math, all you need are rationals. but even if you had some magical computation device that could have pi to perfect precision and e and all those irrationals, you still wouldn't have the kind of continuity of a real line."

Many people have written you off as a troll. I, however, don't have that much faith in people; I think you are genuinely very confused and scared of the world around you. Let me try to help you with that.

You won't tell me about yourself, so let me tell you about me, in hopes that it will lend weight to my words. I am getting a Master's in Computational Nanoelectronics, so I am rather familiar with:
1) Pure mathematics as it relates to Quantum mechanics, and
2) Numerical analysis, particularly Finite Element methods, mesh generation techniques, and various approximation techniques.

You don't seem to understand what the point of doing math is if every step isn't immediately applicable to the real world. That is a position I sympathize with. You are right that, in the real world, nothing has infinite precision. That is a limitation we need to accept and deal with. However, it isn't just irrational numbers that don't have infinite precision in the real world: rational numbers don't either. When I write the number 3, what I really mean is 3.000.... But, what a computer sees (assuming double precision floating point) is 01000000010000000000000000000000. This is an inexact approximation. Now, for the number 3, it really doesn't matter, but when you're dealing with a lot of large (or small) numbers and manipulating them a lot, you can quickly cause lots of errors (floating point errors, among others).

The whole point of Math is to stay out of reality as long as possible. Only at the very last step do you cross the boundary from math to reality, thus making your answer as accurate as possible. It is much better to assume infinite precision until the last step, then you continually round numbers the whole way.

My entire thesis is based on this, actually. I'm trying to solve the Schrodinger equation for electronic structure calculations. My method follows most other's, but they cut out a step early and go to approximations. I stick with the math one step longer, so I'm able to come up with more accurate results. For a long time, it was OK (or impossible not) to cut out that last step. Computers weren't good enough and devices were big enough it didn't matter. Now it does matter, so we need to really on pure math longer, until we get to the ultimate nitty grits of actually solving the equation (at which point the answer is no longer exact). But, if you didn't stick with the math as long as you could, you'd come up with some really bad answers.

uh huh. better ask your advisor about infinite sets. seems like you missed something important there.

Wait, he said "irrational"? I read that as "imaginary". No, I don't know what Gobble was saying in regards to 2nd order infinity for irrational numbers.

here's a Schroedinger's protip for you abge.

The fking cat is ALWAYS dead.

@bolshoi- You are right that gobble's post that you keep quoting should say "The rational set is countable." You don't really have a leg to stand on otherwise; abge just had a great post that I would refer you to.

Side note: The set of constructible numbers sort of describes what you seem to want the "reals" to be, so maybe check those out:

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

oh wait, maybe i misread his statement a bit now that i look back on it. i thought he said rational numbers were 2nd order infinity. hahaha. ok well i understand basically your thesis. but whether you keep things algebraic or convert to a particular representation doesn't affect your abstract representation of the number line.

no, that constructible number has to be made with a straight-edge and compass. but i allow for numbers like e.

I'll be sure to directly wire the International Mathematical Union to make sure they are aware it's still OK to use e.

actually he did say rationals were 2nd order infinity equal to a pair of integers, but later said the size of integers equals rationals. i don't know. maybe he just made a bunch of typos.

but you have to admit that your thesis has nothing to do with the issue of the inclusion of impossible to exist reals in the real line.

I really appreciate how bolshoi "allows" special numbers in his heart to be whatever he wants it to be.
.9 repeating is not 1, but .3 repeating is okay as 1/3.
1, 2, 3 and such: real, but negative numbers: ain't. Let's get real here, ain't no negative numbers in real life.

I bet as a Diplomacy player you would ask to be supported into Spain (nc) from Wmed because it's too complex to play by the rules of the game.

No, but it has everything to do with using impossible numbers to express real-world things. I have pages and pages of math of integration over complex contours, imaginary math in real-space, basis-functions not in real-space. It's a fucking mess. But it all comes together to make a pretty picture of a real atom (or 10,000 atoms, if you wish). It's the same principle as "why are there impossible numbers on the number line". Because math is an abstraction.

@bolshoi- You really have no ground to stand on including e or pi and not including other reals. You just don't.

note that if he had said irrationals were "2nd order infinite", and by irrational he meant R-Q, then that would have made some sense, since the number of reals is much larger than the number of integers.

which other reals are you talking about uclabb? i tell you what, any real you can name, i'll put into my line! it's all taken care of.

the numbers i don't want are numbers you cannot comprehend (nor can anyone else) because they cannot exist in our universe.

What about root(2)? I use that one a lot. Or, do I have to settle 1.4142 in all my calculations?

it's in there! and i'll also throw in pi*e*root(2)! that's 3 irrationals at once! sweet!

i might exclude 5 though. i'm not sure i like that number.

"I bet as a Diplomacy player you would ask to be supported into Spain (nc) from Wmed because it's too complex to play by the rules of the game."

Wait, isn't that move allowed? By the same logic that:

Spain (NC) -> Por
Por -> Spain (SC) bounces.

haha I'm probably wrong but just clarifying.

That's very reasonable of you. Surely, you must agree that it would be unfair to other numbers to only include root(2). So, will you also allow

x^(y/z) ∀ x,y,z ∈ R_bolshoi, where R_bolshoi is the name I've given to your set of numbers.

you got some fancy letters there. but yes, R_bolshoi is BADASS, it's closed under all known operations.

Bolshoi, what you are saying makes no sense. Inf fact, you aren't saying anything. What do you mean by exist? It is impossible for me to draw a line of length pi, so it seems to me like pi probably doesn't exist. A lot of stuff converges to e, but to say anything in real life actually is e doesn't make sense either.

and even future operations! it's closed under any possible operation anyone could ever construct.

hell, why even restrict it to numbers? but i guess that might make things helpful... so i will have R_super_bolshoi that one also includes character strings, superbowl tickets, and bacon.

uclabb, what i'm saying is you take the orthodox real line, take out all the numbers anyone could ever imagine in that line, you're still left with, essentially the same line. all the number that could ever possibly exist or be imagined up is only a countable set. which is nothing compared to an uncountable set.

hang on uclabb, let abge work his magic. He'll be exposed as a fool or a troll before abge is done with him :P

It's smacking of linear algebra to me and thus have already lost interest lol I hate that shit.

"it's closed under all known operations."

Oh, that's good. So, basically R_bolshoi ⊆ R and R ⊆ R_bolshoi. I'm glad we cleared that up.