jbluestein
Level: Smitemaster

Rank Points: 1670
Registered: 12-23-2005
IP: Logged

zex20913 wrote:
Proof:

Try to list out all numbers (rational or not) and have them in a column. For rational numbers, include the trailing zeros.

E.g:

.378213460000000000...
.823479879283458237...
.283789125903045721...
.129039784823487952...

And so on. You have listed a countable number of real numbers between zero and one. (They're in a list!)

However! I can give you a number between zero and one that you did not list! For the nth digit of my number, I will add one to the nth digit of your nth number. (Nines go to zeros)

Using the example above, I would be choosing .4341...

Since this number differs from each number in your list, it is a number between zero and one that you don't have in a one-to-one correspondence with the natural numbers. Thus, the quantity (cardinality) of real numbers between zero and one is greater than the quantity (cardinality) of natural numbers.

Euler would be proud!

(although, really, you used too many digits...)

____________________________
"Rings and knots of joy and grief, all interlaced and locking." --William Buck

brian_s
Level: Smitemaster

Rank Points: 587
Registered: 05-27-2004
IP: Logged

Sorry about posting this so late, I lost my internet connection for a few days.

I got all the PMs and the results are

Player          Num  +/-Av  Pts
-------------------------------
[Average]       64.6
12th Archivist  55    -9.6  9
Snacko          50   -14.6  3
Chaco           80   +15.4  2
Maurog          82   +17.4  2
Jatopian        46   -18.6  1
TripleM         46   -18.6  0
blorx1          85   +20.4  0
The Stew Boy    40   -24.6  0
NiroZ           97   +32.4  0

12th Archivist is the latest person eliminated. That brings point totals to:

Round 7         Total
---------------------
Lamkin          19 X6
Rheb            17 X4
12th Archivist  17 X7
UrAvgAzn        16 X2
Bombadil        15 X1
RoboBob3000     15 X5
Someone Else    14 X3
---------------------
Jatopian         9
Snacko           9
The Stew Boy     7
TripleM          7
Maurog           7
Chaco            5
blorx1           4
NiroZ            0

This round went well, so round 8 begins now. Like this last round, send a PM titled Greed Round 8 with a number 1-80 and one of rock/paper/scissors in the message.

Lamkin
Level: Smitemaster

Rank Points: 606
Registered: 08-17-2008
IP: Logged

brian_s wrote:
The new goal is to be close to the arithmetic mean of the numbers submitted.

The thing is, what does that goal have to do with greed? I liked the old system much better, dammit, because I felt greedy whilst playing the game.
Oh, and NiroZ's last number was greater than 90. What's up with that? There's always one, isn't there?

TripleM
Level: Smitemaster
Rank Points: 1373
Registered: 02-05-2003
IP: Logged

Lamkin wrote:
The thing is, what does that goal have to do with greed? I liked the old system much better, dammit, because I felt greedy whilst playing the game.

Same My whole strategy depended on the fact I could guarantee first place (or at least first equal) any round I wanted.. now my whole strategy is ruined. Oh well, maybe next game.

hyperme
Level: Smitemaster

Rank Points: 1067
Registered: 06-23-2006
IP: Logged

How do your even plan getting close to the mean? The new goal: pick a random(ish) number and hope.

____________________________
[Insert witty comment here]
Qzvlkx?

TripleM
Level: Smitemaster
Rank Points: 1373
Registered: 02-05-2003
IP: Logged

Lamkin wrote:
Oh, and NiroZ's last number was greater than 90. What's up with that? There's always one, isn't there?

Hey, good point! That one should be disqualified, then I'll get some points