Conquer Club

TheProwler wrote:

AAFitz wrote:Infinity is only a theory after all.

Give this man a Gold Star. Come join me (and a few others) at the front of the class.

He could certainly use the education, your technique is formidable. I mean, not really, this wouldn't pass muster in most places, but you've managed to find an educated, gullible audience. I'm impressed that this trolling has lasted 14 pages. I don't believe anyone is stupid enough to believe that decimal representations of real numbers are unique, or at least not stupid enough to keep believing it after 200 posts, but somehow you've managed to string people along into believing that you are that stupid.

7/10 for trolling
0/10 for math
0/10 for philosophy (for joint project with Klobber)

Do threads still get locked around here? Or is this the new wasteland that Flame Wars used to occupy?

sully800 wrote:It's not asymptotic though, it IS 1. Exactly equivalent and interchangeable with the number one.

If you plot the series 9/10 + 9/100 + 9/1000 ... it will asymptotically approach 1.0, that is true.

But 0.999recurring, by definition, is a number with infinite 9's following the decimal point. The number doesn't change as you add more levels of accuracy, and it doesn't approach anything. It simply is a number, and it is equivalent to 1.

So...you are saying

9/10 + 9/100 + 9/1000 ...

does not equal

0.999recurring????


Nice work. Your offense was too great....how's your defense?

sully800 wrote:1/11 = 0.090909...
10/11 = 0.909090.....

1/11 + 10/11 = 1

0.090909... + 0.909090... = 0.999999

1 = 0.999999

QED

Need more?

Haha! Your expressions of 1/11 (0.090909...) and 10/11 (0.909090.....) are not precise enough. If you could someone show the proper level of precision, you would get

0.090909... + 0.909090... = 1

And nobody is arguing that 1<>1.

e_i_pi wrote:You can't simply say 0.333... = 1/3 without giving proof. It is a representation, it is not a proof. Saying that it is true does not prove it is true, otherwise I could say the world is flat. You need to define "..." Now, the only mathematical way to define "..." is to say that it is an infinite series of smaller and smaller decimals. If it is an infinite series, then you can prove 0.999... = 1 and 0.999... != 1, as has been shown above. The correct answer to this question is "mu".

Come up to the front of the class. Those kids at the back are working in a proof without using their favourite symbol: ...

But so far they've only come up with 1/3 + 1/3 + 1/3 = 1

A while ago they had a good laugh when I said one .333recurring <> another .333recurring.

Jolt Cola came spewing out of their nostrils!



It was way cool.

Wow a quintuple post followed by a triple post. The trolls got word that the mods were on holiday.

baldadonis I'd give them 9/10 for trolling - 14 pages is very impressive. I even pointed that out on p10 but they ploughed right through it. I think a quintuple post is prowler's way of checking to see if the mods really are asleep or not. Who knows where we'll end up from here! Maybe stoneham finally tracked down nightstrike?

They do always make the misbehavers and people with glasses sit up front...

xelabale wrote:Wow a quintuple post followed by a triple post. The trolls got word that the mods were on holiday.

baldadonis I'd give them 9/10 for trolling - 14 pages is very impressive. I even pointed that out on p10 but they ploughed right through it. I think a quintuple post is prowler's way of checking to see if the mods really are asleep or not. Who knows where we'll end up from here! Maybe stoneham finally tracked down nightstrike?

Let's try to keep this on-topic.

TheProwler wrote:

xelabale wrote:Wow a quintuple post followed by a triple post. The trolls got word that the mods were on holiday.

baldadonis I'd give them 9/10 for trolling - 14 pages is very impressive. I even pointed that out on p10 but they ploughed right through it. I think a quintuple post is prowler's way of checking to see if the mods really are asleep or not. Who knows where we'll end up from here! Maybe stoneham finally tracked down nightstrike?

Let's try to keep this on-topic.

nah i'm cool with this line of discussion bro

There appears to be some confusion between real and rational numbers

0.999... is real but not rational.

If 0.999... is not equal to 1, then it follows that there must be another number between them. I will give a lifetime supply of premium membership to the first person to find it.

MrBenn wrote:There appears to be some confusion between real and rational numbers

0.999... is real but not rational.

If 0.999... is not equal to 1, then it follows that there must be another number between them. I will give a lifetime supply of premium membership to the first person to find it.

ε

Now where's my lifetime premium?

ε² = 0 [ε ≠ 0]

.9² = .81

1² = 1

ε is a lot smaller than 0.999.... , and is clearly not between it and 1.

0.999... and a bit.

Moneeeeey! Hand over me membership

How big a bit?

MrBenn wrote:ε² = 0 [ε ≠ 0]

.9² = .81

1² = 1

ε is a lot smaller than 0.999.... , and is clearly not between it and 1.

DOES NOT COMPUTE.

You do know what epsilon represents right?

e_i_pi wrote:

MrBenn wrote:ε² = 0 [ε ≠ 0]

.9² = .81

1² = 1

ε is a lot smaller than 0.999.... , and is clearly not between it and 1.

DOES NOT COMPUTE.

You do know what epsilon represents right?

An arbitarily small amount...

Either that or the number 5.

MrBenn wrote: 0.999... is real but not rational.

lol

MrBenn wrote:How big a bit?

You know, some. Hand it over.

Here you go:

[1,0] is a closed set. In this set all real numbers between 1 and 0 are included.

(1,0] is an open set. In this set 1 is not included, but .999.... is.

How can two numbers that are equal not be in the same set? It is because they are not.

Here is why:

A set S in Rm is open if for each xεS:
Ǝex>0:Bex(x)cS

Al l .99… does is make ex ¬ infinitely small, but it still is bigger than 0.

Therefor these two numbers are not equal.

Suspect101 wrote:Here you go:

[1,0] is a closed set. In this set all real numbers between 1 and 0 are included.

(1,0] is an open set. In this set 1 is not included, but .999.... is.

How can two numbers that are equal not be in the same set? It is because they are not.

Here is why:

A set S in Rm is open if for each xεS:
Ǝex>0:Bex(x)cS

Al l .99… does is make ex ¬ infinitely small, but it still is bigger than 0.

Therefor these two numbers are not equal.

wow great tautology bro

Suspect101 wrote:Here you go:

[1,0] is a closed set. In this set all real numbers between 1 and 0 are included.

(1,0] is an open set. In this set 1 is not included, but .999.... is.

No it isn't.

1-.999...= .000... (infinite number of zeros) 1

Since there is an infinite number of zeros then the one is never reached, so at every point except those greater than infinity 0.999...=1. Since you can't get greater than infinity then 0.999...=1.

pmchugh wrote:1-.999...= .000... (infinite number of zeros) 1

dear god will you people please stop doing this shit

Snorri1234 wrote:

Suspect101 wrote:Here you go:

[1,0] is a closed set. In this set all real numbers between 1 and 0 are included.

(1,0] is an open set. In this set 1 is not included, but .999.... is.

No it isn't.

It is by the definiton of an open set:

A set S in Rm is open if for each xεS:
Ǝex>0:Bex(x)cS

Just because you say it isn't doesn't mean shit. Prove that it isn't.

Suspect101 wrote:

Snorri1234 wrote:

Suspect101 wrote:Here you go:

[1,0] is a closed set. In this set all real numbers between 1 and 0 are included.

(1,0] is an open set. In this set 1 is not included, but .999.... is.

No it isn't.

It is by the definiton of an open set:

A set S in Rm is open if for each xεS:
Ǝex>0:Bex(x)cS

Just because you say it isn't doesn't mean shit. Prove that it isn't.

Because 1 and 0.999... are equivalent. There is no difference between the two numbers, not even ε. You are defining 0.999... to be smaller than 1 here, and then saying that it is proof that its smaller than 1 because they are not in the same set. But if they are equivalent, then your statements are false and the are indeed equal. Defining the numbers by sets like that will not work, since your definition determines the outcome.

sully800 wrote: Because 1 and 0.999... are equivalent. There is no difference between the two numbers, not even ε.

There is a difference, ε.

sully800 wrote: You are defining 0.999... to be smaller than 1 here, and then saying that it is proof that its smaller than 1 because they are not in the same set. But if they are equivalent, then your statements are false and the are indeed equal. Defining the numbers by sets like that will not work, since your definition determines the outcome.

This is not a made up definiton, this is the FORMAL DEFINITION that you will also find in any advanced number theory, finite and infinte calculus, matrix algebra, or any other kind of text you will find.