Mobius

"at least ONE of them must be a fraction" means one or two may be a fraction Doesn't matter of 2 of them are fractions, this just strengtens the case. 1/a>b+c say a=1/3, b=1, c=2 That is true, in this case 1/a = b + c However there are two more numbers to be added to that 1/a (or b/a) as it would be. Now I did say it would be greater but as you showed it could be equal, however as there are 2 more numbers to be added to it, it will always be greater...

Interesting. According to the train, it sees a fly stop relative to it. According to the fly, it sees the train stop relative to him. The problem is for the outside observer, when he sees the fly come in contact with the train. Perhaps a shock wave is sent through the train accomodating this infinitesimal stopage! Man it's terrible when Zeno (Xeno) raises his ugly head, he did the same in my flashing light bulb problem on the maths thread:-) Thank god the real world stops these mad situations happening....

I am not quite sure what you mean but if forces are added from different directions then they will not always add up to their linear sum. In other words, if you and your friend are pulling an object with a force of 1 N, but you are pulling at right angles, then the object will move forward, at 45 degrees between you and your friend with a force of 1.4 N not 2 N. I don't know if this is what you meant or not?

Ah come on, J.C.MacSwell, you can do better then that... As I said neglect air resistance, pretend it happens in vacuum, (yes I am aware that a fly could not fly in a vacuum). you still haven't pointed out the flaw in the argument.... You can't just highlight what I said and say it's wrong, why is it wrong???

Here we go... A fly is flying about, minding its own business. However he does not realise he is on a direct collision course towards ano on coming train. Now neglecting air resistance, when he hits the train he becomes a part of it right? At that very same moment he must change his direction. However in order to change direction he must STOP, now as he is part of the train the train must also STOP for that brief second.... Therefore a fly can stop a train, now where is the flaw in this argument....?

Your last equation 0 > (c-1)a^2b+(a-1)b^2c+(b-1)ac^2, would make sense if a, b and c were ALL fractions, but as I pointed out in my last post only 1 of them has to be a fraction (according to the original conditions). I think my proof is fine but it may have a flaw... Awaiting confirmation!!!!

(c-1)a2b+(a-1)b2c+(b-1)ac2 And how are you proving that this is a negative number? I don't seem to be ble to solve this inequality mathematically BUT I can solve it logically. In order to satisfy a*b*c<0 where they are all positive values then at least ONE of them must be a fraction and the other two numbers cannot multiply together to be greater than the denominator. e.g. 1/20, 3, 5... When multiplied this gives 3/4. Now:- a/c + b/a + c/b > a+b+c On the left hand side a, b and c are all denominators, one of them will be a fraction (say a) and as it is on the bottom line it will be inverted and will be large. It will also be larger then the other two numbers added together (b + c) due to my logic above (a*b*c<0). i.e. if it is larger than the product it will be larger than the sum. So the right hand side will be b + c plus the fraction which will be smaller than the left had side. Of course if a, b and c are all fractions then this inequality is obvious as when fractions are divided the answer is always greater (or equal) then either of the two fractions to begin with. this is not very mathematical and I'm sure if there is a flaw in my logic it will be pointed out.... It is a logical proof however (I did try for a mathematical one!).

Did you read the original post?

Ah yes RICHARDBATTY, but I think we are well passed practicallity here and talking about the theoretical. In other words, what if the light bulb was not restricted by the limitations of physics i.e. the motion of electrons limited to 10^(-18) seconds. I was going to shorter time spans of 10^(-43) seconds where maybe our theoretical lightbulb may break down....

The last number in 10/3 would be 3 as all the previous numbers are 3 but as you pointed out earlier, there is NO last number of 10/3. So this is not the same as the flashing light bulb problem. It is obvious that the sequence provided is inadequate to describe the nature of the bulb at and after the limit of 2 minutes. I cannot see how you can define your cycles. Physics may be able to explain it with discrete time or maybe a 'tunnelling effect'??? close to the 'barrier' (limit). But maths (as defined here) cannot solve the problem. Regardless of the solution if this does happen your light bulb, stick around for 2 minutes to see what happens then buy a new one ;-)

Also if you want to carry your square wave idea to the limit, then at the two minute mark it is just a line with 'on' represented at the top and 'off' at the bottom.

Okay, fair enough guys, much more thought went into this than I had originally thought. So to summarise, Matt can give me models for the light bulb being on or off as there is not enough information available i.e. there is only enough information to define its state at some finite time before 2 minutes. YT2095 sees it as a binary progression, so if it is on at 1 minute (odd number) it will be the opposite at 2 minutes (even number) i.e. off, regardless of intervals in between. All good, thanks for the information guys...

I think you have oversimplified the situation. you are thinking of finite counts. This is not a finite count. The time intervals between the flashes become shorter until they reach their limit of 0 at the 2 minute mark. therefore technically being both on and off which is an unacceptable situation. The chess board and binary count you are talking about are based on finite counts.

yes I do understand an infinite sequesnce, what I don't understand is what happens when the limit of an infinte sequence is reached and we are not talking about 1 million years, we are talking about 2 minutes....!

Ah yes some interesting points there on time. If time was discrete it would solve our problem, as I hinted at earlier. The 10^(-43) seconds is Planck time and the associated length is Planck length (1.6*10^(-35)m). Shorter time intervals are not understood, it doesn't necessarily mean that they don't exist. Sure we could always abandon time altogether and believe (like physicist Julian Barbour does) that time doesn't exist and we live in a world of 'nows'. Matt, I get your point, just not sure how to add information that you say is lacking. I set initial conditions and allowed time to evolve, I don't see where any further information is required. this is probably due to my lack of maths skills (or rather my way of looking at maths). My trusty computer does most of my maths for me;-)

Well it looks like maths doesn't have a solution to this question ;-)

ok, I see your point... I also see how maths and physics should have a restraining order... Nothing in maths forces time to 2 minutes (in this senario anyway). but in physics there is nothing to stop the 2 minutes approaching. Just as a bizzare twist to this post. If this flashing light bulb was happening at the event horizon of a black hole then the time would slow down and eventually become 0 (according to us) thus satisfying our required condition. Of course according to the lightbulb time would seem normal...! I don't know where this thread is going but it seems that such an unassuming question has many problems....;-)

If your doing a search for xenos paradox, spell it Zeno's paradox!!!

True, I am more interested in the maths as it has been establised thta the situation cannot happen. In your example x satisfies x(t)=1/t for all strictly positive t. what is x(0), there is nothing forcing the t to 0. In the case of the flashing light bulb time is forcing the function f(t)=0 to f(2), (unless time stops of course and it never reaches the 2 minute mark, but I wouldn't want that situation to arise... it would however solve our problem ;-).

From a physical point of view it would not appear at half brightness. you would (after a short amount of time) see it on fully. this is due to 'persitance of vision'. We cannot differentiate between flashes of about 20 per second. A real light bulb flashes 50 times a second due to the ac current running through it. We just see it on...

Fair enough, but surely as the limit is reached, there would be no more flashing?

There are lots of questions in physics where the maths breaks down. The beginning of the universe at the big bang, the singularities in black holes, travelling at the speed of light (your time passed effectively become 0) and so on... These questions deserve a physical description. The flashing light bulb problem is loosely based on zeno's paradox but it is based on time rather than distance and motion. Whenever infinity raises its ugly head in our finite world it always casues problems. It seems that the physical world solves this problem (maybe by not allowing the situation to happen in the first place). When we discuss the start of the universe we generally say it started at t=10^(-43) seconds as the physics before this is not understood, maybe as I stated already that if we had such a light bulb than as the interval between the flashes became this short than it may jump to a final state. As for after the two minutes it stands to reason that it will remain in the same state that it was at 2 minutes as the interval between the flashes is 0. The answer is not altogether important, but the question is!!!!

Just because it cannot happen physically, that does not mean we can't speculate theoretically what would happen. I feel the question poses a challenge and is worth considering. That is the reason I posted it on a maths thread as physics (my background) generally dismiss this question as invalid....

I think the problems come into the case when the time intervals between the flashes becomes very short. Perhaps when the time interval reaches Planck time, 10^(-43) seconds, the light bulb will move into one of the states, meaning that it did not have to flip states an infinite amount of times. Alternatively it could be "on" in our universe and "off" in an alternative universe (satisfying the condition of being both on and off at the same time) after flashing an infinte amount of time (according to it) but a finite amount of time (according to us) ;-) I was wondering whether to post this in the maths or physics section, glad I posted it in the maths one:)

I have asked this question before but have never really had a satisfactory answer to it, so I will throw it out here and see what happens. the problem is based on a faulty lightbulb that flashs. However it's flashing is based on the infamous infinite sequence 1 + 1/2 + 1/4 + 1/8 ..... i.e. the light is on for 1 minute and off for 1/2 a minute, goes on for 1/4 of a minute and off for 1/8th of a minute. Now it is well known that this sequence never reaches 2. Therefore at two minutes is the bulb on or off???? Now I'm well aware that this could not physically happen due to the nature of a light bulb, but I want a theoretical answer! i.e. the ideal light bulb, or an electron flipping from state spin up to spin down.