I'm saying they're equal. Which you admitted when you closed it under every operation.

for one, you agree that R is uncountable. if you looked at R_bolshoi's definition, and thought about it, you'd see that it's actually countable.

I don't see how. I can make any number in R from numbers in R_bolshoi following your rules.

the second was saying R is a subset of R_bolshoi, i didn't say proper subset. i'm not claiming you said R is a proper subset. but even saying it's a subset is wrong.

i said closed under all operations. you can't take numbers from another number line and then do an operation on it to move it into my line. how the hell are you in a masters program?

or maybe i'm misunderstanding something you said

I'm not taking them from another line. I know what closed means. Give me a number in R and I will make it in R_bolshoi using only numbers in R_bolshoi.

@YJ

I'm glad you saw where I was going with this. Unfortunately, I was a bit rushed (and bolshoi still seems confused), but I'm on my way to a seminar so I can't play games for much longer.

haha! ok now i understand. that's your problem! i'm telling you that you can't!!! because you can only construct a countable set of numbers. assuming you have a finite algebraic expression.

No. You're wrong. You said I can have any operator. Are you not including transcendental functions? I need those to do work.

it's all still countable. i'm telling you. even if you try to cut numbers apart, those cuts will still have to be made somewhere. the decision on where to put the cut is based on something. there are only a countable set of somethings you could construct. i'm not talking about where the cuts are, i'm talking about how many there are.

ok i'm getting kind of tired right now, so i'm not entirely sure, but this article is probably the best way to do further research on R_bolshoi
http://en.wikipedia.org/wiki/G%C3%B6del%27s_constructible_universe

or maybe it's not. oh well too tired to continue. hopefully i'll be in the mood to argue again tomorrow. we'll see.

http://mathoverflow.net/questions/70097/large-cardinals-and-constructible-universe

ok i'm not completely sure what's going on with this one, but it says something about constructible reals so this could be what i want. i'm not sure. abgemacht can enlighten us with its meaning upon his return.

I understand now. He's not a troll, really. Whats the name for the guy who is like a troll but doesn't mind expelling huge amounts of mental energy into his erratic arguments? I know there's a word for it.

Oh, he's an ASSHOLE. It all makes so much sense, now.

No. You said I could have root(2) in R_bolshoi. That has an infinite number of digits, which can only be expressed as an infinite series. The same goes for transcendental functions, which you told me I could have. You lied to me like a used cars salesman overselling his product. That makes me sad :_(

There is a bit of a difference between the used cars salesman and bolshoi's system. The used car will probably still run, not well perhaps but it will still run. Bolshoi's system is internally and externally invalid, not unlike Christians who advocate for the death penalty or the institutionalization of overt and subvert racism.

I suggest that in future dealings with idiot boy here you demand that he address each and every question you direct at him and don't let him change the subject with new idiocies.

@YJ

I have a policy where I try to make my position as clear as possible, if not for people like bolshoi, then for silent readers who may be confused into thinking people like him are correct.

I believe I've made my point as clear as possible (despite the obvious attempts at derailment) and I also believe that no more progress will be made by arguing with bolshoi, so that concludes my discussion with him.

I wish I had that wisdom...

Damn, I missed all the fun. At least I got to avoid abge making me feel stupid too.

omg
if root(2) is acceptable, then surely root(3)? there are infinite no. of square roots that you can create, that are irrational and thus have to be included in R_Bolshoi.
then what about root(root2)? I can construct that easily...hm R_Bolshoi inclouded. What about root(root3)? root(root4)?...... root(root(root2)? etc?

Already there are an uncountable number of square roots you can physically construct with just compass and straightedge. Your definition is invalid.

*sorry that root(root4) was meant to be root(root5)

@Gobble

Please read better. I'm way ahead of you on that line of thought.

lol

That came out a lot ruder than I intended it to.

"there are only a countable set of somethings you could construct"

No, no, no, that is exactly what the Axiom of Choice denies...
and if you do not accept the Axiom of choice then most of your mathematics will not work at all.

@Gobble- The set of all numbers that are contained in a tower of square roots is countable. They are called the constructible numbers, and are what I tried to encourage Bolshoi to adopt, but he decided against it. The set of all numbers in a tower of any integer root is also definitely countable. I'm not 100% sure about closure with any roots like abge was talking about.

every number you can construct with only roots is clearly countable. you can check the first property of algebraic numbers on my favorite website, http://en.wikipedia.org/wiki/Algebraic_number#Properties

ok, thanks for the info
but even so such a number system makes no sense. Why should some numbers be defined and some not?