Photons knocked me out once. Really. So they must be particles.
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Anonymous2008-01-05 15:35
Everyone fucking knows photons are particles. They just behave like waves occasionally, just like electrons, protons, whole atoms, and any number of other smallish particles.
>>71
Yes, but in that one instance, the photons were DOING "the wave", and I just got in the way, and they knocked me the fuck out. So what can we conclude from that?
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Anonymous2008-01-05 17:16
>>72
That you're a white trash stadium crowd type?
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Anonymous2008-01-05 17:19
[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
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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
>>73
No. You fail at reading comprehension. The PHOTONS were the ones doing the wave. I was merely nearby at the time.
I suspect they go all "trash stadium" on their own. I have some photons zipping around my apartment right now, and I'm keeping an eye on them for such sudden behavior.