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Math? Infinity and Zero (pg. 6)
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| Durafei |
Here is interesting question:
Which numbers there are more of: natural(1,2,3,4 etc) or rational(any number of the form a/b where 'a' and 'b' are natural ie. 1/2,1/3, 5/7, 7/1, etc etc)
Answer: There is EQUAL number of natural numbers and rational numbers. Unbelievable, but true.
That's just one example of how weird 'infinity' is. |
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| drizzt81 |
| quote: | Originally posted by trancaholic
Well, that effect really depends on momentum of photons rather than mass, right? You wouldn't expect something heavy to push something else, except if the heavy object was already travelling at some speed (that is, had momentum).
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i am sorry it i was unclear.. yeah momentum is the thing.. since momentum is conserved, u slow the atoms down (recude their momentum) by hitting them head on with something else with a small amount of momentum..
here is a toughie though:
Momentum (linear) = mv (mass * velocity)
now, how can an e- have momentum, but not mass! |
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| drizzt81 |
| quote: | Originally posted by Durafei
Here is interesting question:
Which numbers there are more of: natural(1,2,3,4 etc) or rational(any number of the form a/b where 'a' and 'b' are natural ie. 1/2,1/3, 5/7, 7/1, etc etc)
Answer: There is EQUAL number of natural numbers and rational numbers. Unbelievable, but true.
That's just one example of how weird 'infinity' is. |
yeah i remember that from my 'discrete math' class.. i don't know if i ever saw a proof.. but i think to remember i did.. it was cool |
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| Izzy |
| quote: | Originally posted by drizzt81
here is a toughie though:
Momentum (linear) = mv (mass * velocity)
now, how can an e- have momentum, but not mass! |
i'm sorry, but i was taught that e- (an electron, right?) has a mass of 9.11 x 10^-31 (9.11e-31) [kg] |
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| DjJade |
| quote: | Originally posted by Dmatrox
Where there is mass there is energy and wherever there is energy there is mass. |
not really... ofcorse i am taking this out of context becuase i dont feel like reading the whole thread...but someone asked a question about photons and momentum. photons have no rest energy and no rest mass. its true that momentum is the product of a particles mass and velocity but one must think about photons with respect to relativity.
since all particles exibit both particle and wavelike characteristics, photons infact have momentum, however it is momentum related to energy which is related to frequency in a wave. e=hv and p=h/lamda where v [not english v but the greek letter nu] is the frequency and lambda is wavelength. |
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| mndeg |
zero times infinity
lets see. I have ZERO APPLES, I DECIDE TO MULTIPLY THEM BY INFINITY.
how many do i have now?
none because i never had any to start with |
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| Milhouse |
I hope no one construes this as me being arrogant, but I am in my 4th year of a BSc. in physics so I've actually come across a lot of this.
First off 0/0:
although intially this is undefined, it technically does have an answer... it involves a calculus theorum known as L'Hopital's rule or theorum (I can't remember if it's a rule or a theorum - not a big deal though)... basically any equation like this in the physical world would be the result of some function or combination of functions (essentially some formula)... now what needs to happen is there needs to be a decision on whether the numerator is approaching 0 faster or the denominator is approaching 0 faster... this is done by taking the derivative of the numerator and then taking the derivative of the denominator... this process is repeated until one disappears and we are left with only the numerator or the denominator... if the numerator is left then the denominator approached 0 faster, and therefore the answer is infinity... if the denomenator is left then the numerator approached 0 faster and the answer is simply 0... so there is an answer to this... although I have never encountered an answer to the 0^0 problem that was posed so that one has me scratching my head.
Secondly Absolute 0:
drrzt81 was right in saying that you can never reach this point... this relates to a few fundamental theories of quantum mechanics, essentially the coolest point something can obtain is to basically eliminate all but it's spin potentials... and then you would align the spins of all of the atoms in the material... this produces what is known as bose einstein condensate... a material which essentially is in the lowest possible energy state... to really understand this you need to understand a few really complex things, stuff that is even confusing and mystical at my level of math and science.... so I'm not going to get into the gory details, partially for fear of getting it wrong, but the bottom line, absolute zero is a limit which materials can approach but they will never obtain because all atoms have an intrinsic spin associated with them....
Third Photons and mass:
photons have no mass, if they did have mass, the universe would essentially fall apart and we wouldn't exist, so we are pretty lucky that they don't have any sort of mass.... the reason for this is that photons act as something called a moderator... the essentially are passed back and forth by sub atomic particles and it is this passing that actually produces the electromagnetic force... essentially it is theorized that all forces are cause by a moderator of some sort, it has been shown that photons moderate electromagnetism, and pions and muons moderate strong nuclear force, antineutrino's moderate weak nuclear force... and it is postulated, although there is no evidence of this that there is a particle called a gravitron that moderates gravity... anti-neutrino's muon's and pion's all have mass and therefore have a life span so the force can only act over a certain distance, that is why atoms can only get so big, after a while the strong nuclear force can't traverse that distance and the nucleus of the atom falls apart... photons being massless can travel for an infinitely long time, hence the reason that the electomagnetic force extends forever... so if photons had mass then the electromagnetic force would act over a given distance and it would cause parts of the universe to move away from themselves... subsequently it would cause the big problems.... photons do have momentum though, I forgot the equations as to why though... it's at home somewhere...
finally, I haven't provided a thorough representation really of any of these ideas, to have these really make sense you need to see the equations as they say more than words ever could.... the problem is a large portion of the population doesn't have that kind of math background.... also I really didn't feel like typing out the whole idea... this just scratches the surfaces of theories that took me 4 long years to learn... |
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| fate |
| quote: | Originally posted by Dmatrox
a = m/s/s
v = m/s
d = m
distance is not measured respect to time. distance is distance. When you travel you measure in distance (m), but if you want to know your velocity through your distance, you involve time ;) What im wondering is, whats after acceleration since a=m/s/s, so presuming the pattern, ?=m/s/s/s |
hehe :p
you just get an accelerated acceleration, that means that a (accel) is a function of the time -> a(t)
by integrating the function you get the speed
integrate another time you get a function for the distance
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:D |
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| trancaholic |
| quote: | Originally posted by Milhouse
I hope no one construes this as me being arrogant, but I am in my 4th year of a BSc. in physics so I've actually come across a lot of this.
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Of course not. I myself have one bsc (except 6 months) of maths behind me, 12 months of concentrated physics, and 53 months of data theory (A<=>no repeats) additionally, but what kind of legitimization does that provide?. There's several people on TA with technical background. Why don't you read the entire thread before posting? Several of your points have been mentioned more than once, and I fail to see why your post is relevant? Perhaps we could achieve some kind of equilibrium, instead of claim after claim?
Sorry to sound like a bastard, but I really hate when people fail to read the entire thread before posting. When it's a political thread it is excusable, but fact threads like this is plain lazynes... |
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| Milhouse |
| quote: | Originally posted by trancaholic
Of course not. I myself have one bsc (except 6 months) of maths behind me, 12 months of concentrated physics, and 53 months of data theory (A<=>no repeats) additionally, but what kind of legitimization does that provide?. |
Wasn't trying to provide legitimization, it was just a precursor to the knowledge that I was about spew. It's always important to understand why, so why do I know this, because I took the courses. Nothing more nothing less. If someone read more into it than that, then they missed my point.
| quote: | | There's several people on TA with technical background. Why don't you read the entire thread before posting? Several of your points have been mentioned more than once, and I fail to see why your post is relevant? Perhaps we could achieve some kind of equilibrium, instead of claim after claim? |
I felt my claim was relevant because I provided some insight that hadn't been mentioned. I did repeat other people's ideas and statements, but honestly only for the purposes of clarity and to provide a basis for continuation onto each of the thoeries. I didn't want to leave more bits and pieces lying around in a mess. I'm a little taken back that my post was construed as irrelevant.
| quote: | | Sorry to sound like a bastard, but I really hate when people fail to read the entire thread before posting. When it's a political thread it is excusable, but fact threads like this is plain lazynes... |
I read about 90% of the thread, honestly I don't have the kind of time to make sure that I absorb every little detail. I'm also a little curious as to the difference in a political thread vs a facts thread. Redundancy is redundancy regardless of the topic it's being used in. |
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| astroboy |
| FOr the record I thought Milhouse's post was interesting and valuable. |
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| milanster |
if u take 1/inf to be zero and inf to be inf
zero * zero = 1/inf * inf = inf/inf = 1 :D
that was just a stupid assumption...did anybody actually know that 1 to power inf equals 'e' ? which is 2.718281828 :p |
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