he has tenure so he can say what the fuck he wants for $$$ lolololol
Name:
Anonymous2007-12-22 20:51
∧＿∧ ／￣￣￣￣￣￣￣￣
（ ´∀｀） ＜ im table cat! michio kaku is right my other parts are scattered in a parallel dimension due to a malfunctioning teleportation over matter hax
／ | ＼＿＿＿＿＿＿＿＿
/ .|
38 Name: Anonymous : 2007-12-20 03:55
41 Name: Anonymous : 2007-12-21 17:41 we could be in the middle of intergalactic communication and not even knowing it!!
O SHI-!
42 Name: Anonymous : 2007-12-21 18:15 >>41
michio kaku is my new god
43 Name: Anonymous : 2007-12-21 18:15 he has tenure so he can say what the fuck he wants for $$$ lolololol
Michio Kaku builds Quantum Computar, using only his left hand.
Name:
Anonymous2007-12-24 20:02
sdfghn
Name:
Anonymous2007-12-24 20:37
∧＿∧ ／￣￣￣￣￣￣￣￣
（ ´∀｀） ＜ IF U WERE KILLED TOMORROW IN A TABLE-RELATED ACCIDENT, I WOULDNT
／ | | GIVE A RATS ASS BECAUSE I WOULD BE SITTING ON MY TABLE!!redcream look at this please
Michio Kaku On Aliens, On Physics ... http://youtube.com/watch?v=uWW6_LfiJJk http://youtube.com/watch?v=PW8rgKLPHMg
/ .| ＼＿＿＿＿＿＿＿＿
/ "⌒ヽ |.ｲ |
＿＿ | .ノ | || |＿＿
. ノく＿＿つ∪∪ ＼
＿（（＿＿＿＿＿＿＿＿_＼
￣￣ヽつ￣￣￣￣￣￣ | |￣
WE TRUE TABLECATS
WE SIT TOGETHER
WE SIT TOGETHER ON A TABLE
send this TABLECAT to everyone you care about including me if you care. Count how many times you get this, if you 1000GET, then you're A TRUE TABLECAT!
∧＿∧ ／￣￣￣￣￣￣￣￣
（ ´∀｀） ＜ IF U WERE KILLED TOMORROW IN A TABLE-RELATED ACCIDENT, I WOULDNT
／ | | GIVE A RATS ASS BECAUSE I WOULD BE SITTING ON MY TABLE!!redcream look at this please
Michio Kaku On Aliens, On Physics ... http://youtube.com/watch?v=uWW6_LfiJJk http://youtube.com/watch?v=PW8rgKLPHMg
/ .| ＼＿＿＿＿＿＿＿＿
/ "⌒ヽ |.ｲ |
＿＿ | .ノ | || |＿＿
. ノく＿＿つ∪∪ ＼
＿（（＿＿＿＿＿＿＿＿_＼
￣￣ヽつ￣￣￣￣￣￣ | |￣
WE TRUE TABLECATS
(Post truncated.)
Name:
Anonymous2008-01-01 18:19
∧＿∧ ／￣￣￣￣￣￣￣￣
（ ´∀｀） ＜ im table cat! michio kaku is right my other parts are scattered in a parallel dimension due to a malfunctioning teleportation over matter hax
／ | ＼＿＿＿＿＿＿＿＿
/ .|
>>67
Nuh-uh, I'm the real me. Those guys are the same fag.
Name:
Anonymous2008-01-05 17:18
[4:25] Rational numbers as a countable infinity
1 Name: MathMajor : 2004-12-27 13:40
This past semester I took the first halves of Introduction to Analysis and Modern (Abstract) Algebra in which, naturally, we covered the basics of the cardinalities of infinities. I understand the concepts of what makes something countable verses uncountable. I simply have an intuitive problem with the fact that the rational numbers are countable. The other basics countable infinite sets (Integers, Evens, Odds, Natural Numbers, etc.) all sit well with me. For some reason, I just have a problem accepting that the Rationals are truly countable. I understand that a definition is not arguable, but it just does not feel right.
Part of my discontent lies in the fact that like the continueum, there is no smallest positive rational number. This is not true for the previously mentioned sets. I feel that the rationals are somehow set apart from this set. If I recall correctly, it was proven that "It cannot be proven nor disproven that there exists an infinite set whose cardinality is greater than the cardinality of the countable infinite sets and less than the cardinality of the continueum (the reals)."
If anyone knows where I may be able to find more information on this, or even has an answer to my dilemma, please let me know. Thanks!
-Will
The 5 newest replies are shown below.
Read this thread from the beginning
21 Name: Anonymous : 2008-01-04 18:15
FLOOD
22 Name: Anonymous : 2008-01-05 01:18
But how are they less than the infinite complex numbers.
23 Name: Anonymous : 2008-01-05 01:59
old thread is old
24 Name: Anonymous : 2008-01-05 10:56
They are both countable, just the rationals are not well order with the operator (<)
Imagine it this way, if we define every even integer n to have "size" 1/n, and then ordered to integers according to this definition we have this list:
....10, 8, 6, 4, 2, 1, 3, 5, 7, 9.......
there is no least, and no greatest number, very much resembling the rationals.
There are ways of ordering the rationals such that there is a "least member" just that the ordering isn't using the operator (<)
The fact that they have equal cardinality is obvious consider the injection f from Q to Z