pulkit

The statement of third law I always knew was that "the absolute entropy of a perfect crystal at absolute zero is zero" . I do think that this is highly unlikely because a lot of theories and laws would suggest that it is IMPOSSIBLE.

1. Write down a balanced chemical equation for the redox reaction b/w the reagents mentioned. 2.Then by using the ratios in which the chemicals react, you can answer all those questions.

When i[2] goes from 1 to 1, all subsequent loops will also go from 1 to 1. For example, i[3] will go to min{i[2], n-2} which is 1, similarly i[4] will also go to 1. As a result the print statement is executed exactly once hence [MATH]P(1)=P(n-1,1)=1[/MATH] Similarly if you work out for the case when the outermost loop reaches its 2nd iteration, then i[2] will go from 1 to 2. Again if you try to work out you'll see that from the 4th loop inwards all loops will only ever go from 1 to 1 making them redundant. As a result you can reduce the problem to just the loop numbers 2 and 3, which is just the case of P(2). You can discuss generally and show [MATH]P(i)=P(n-1,i)[/MATH]

I would try to relate the surface tension of the liquid somehow to the splatter pattern and size if I were you. if you want to talk about stuff like terminal velocity you need to also measure the diameter of the initial drop, I hope you keep that in mind.

I did not need to put "a number greater than infiinity"(The mathematician in me dies a thousand deaths when I use Lingo like that ) to figure the range out. All I saw was that as I keep putting in larger and larger numbers the function keeps giving higher and higher outputs. In other words, the function is an increasing function, i.e., if x>y then f(x)>f(y). As there is no limit to the hugeness of x that I can choose over the domain of real numbers, there is also no limit to the values that I can get out of the function. Hence I conclude that the function must approach infinity. I do not acctualy need to plug in any numbers into the function, its a purely theoretical arguement. And whenevr you have to determine the range of a function (a very tricky thing to do by the way when you get to complex functions), you either do so graphically or by the type of theoretical arguements I mention. So the question of plugging in "numbers greater than infinity" (sigh !) never arise. I hope I resolved your issue, its bed time for now !

2nd Law of Thermodynamics probably.....thats the one with loads of different statements

THere is no greates number possible....that is the very essence of infinity. We are not trying to look for numbers here. I will use this concept of infinity whenever I want to describe the behaviour of a function. I can then observe that given a set of numbers, what values can my function take. If I realise that there is no largest number in my set, then obviously no metter how large a number I think up, my function can always take a value (finite) more than this. THen I say that the function goes to infinity. You CAN Not call the biggest number possible infinity because if you are talking of a finite set of numbers, the concept of infinity itself is redundant. If you "believe" in numbers only upto 5, you will never evr encounter things that approach infinity.

What do you mean ?

I do not understand what you find so difficult to comprehend. This makes no sense to me. [MATH]\infty[/MATH] may be defined as the tendancy to get larger than any numerical value that one can think of. View this problem in the light of this definition. Hence by saying that a function [MATH]f(x)[/MATH] has a range of[MATH](0,\infty)[/MATH] you have conveyed all the knowledge you ever need to. When you initially start with calculus, the concept of [MATH]\infty[/MATH] is rather an confusing one to grasp, but I am sure that as you are exposed to more problems and concepts you will find what I have said to be completely correct.

No infact it would be totally incorrect because as I pointed out [MATH]\infty[/MATH] is not a number and writing [MATH]\sqrt{\infty-1}[/MATH] would mean you are treating it as a number. Because its a property that a function approaches you ALWAYS say that the function goes to [MATH]\infty[/MATH] and not anything else. To a mathematician [MATH]\sqrt{\infty-1}[/MATH] is just rubbish.

And most importantly, you would have no concrete proof to support your claim.

It won't simply because you can't write a program with a generic number 'n' of loops. You would need to keep modifying the number of loops which would be very tedious and then need to figure out a pattern in the numbers that you get out......a hard task.

That'll not be the right way to do it. Thats the worst way to go about solving theoretical computer science problems, you never learn and hardly ever get anywhere

First of all [MATH]\infty[/MATH] is a property / tendancy and not a number. So there is nothing such as [MATH]x=\infty[/MATH] or [MATH]\sqrt{\infty-1}[/MATH]. And also Range is an interval, not a number so the range of the function you mention is acctually correctly written as [MATH][0,\infty)[/MATH]

All you need is a refractive index gradient, thats essentially what causes a mirage.

If you need to experiment, you might need a material that has a gradual gradient in refractive index vertically or horizontally. Then, by shining light on it (in a proper direction of course), you would in essence create a mirage of your own.

What are sqr and inf supposed to mean ? Check LaTex symbols here

I defined [MATH]P(n)[/MATH] as the number of print statements executed in n loops, with the top most going from 1 to n. Alternatively, it is the required answer in the case when you have n loops. The fact is that whenever there shall be n loops the outer most will go from 1 to n. There is no need to define it as [MATH]P(n,n)[/MATH] because all the terms that come out in the recurrance you mentioned can be reduced some [MATH]P(i)[/MATH]. In fact, [MATH]P(n-1,i)=P(i)[/MATH] for [MATH]i \leq n-1[/MATH] .

I know about the zero point energy, it is simply unavoidable. But, I believe absolute zero is something that can NEVER be achieved. It is a theoretical and practical limit to the temperature scale which can at best be approached assymptotically.

If you are not observing, how else will you get back your message ? The only way to code n decode is to some how interact with the atoms which would count as an observation.

1.You have a large quantity of gas. 2.Some atoms are excited and they produce light. That is about ebough to interact with other atoms.........its no use getting confused, its as simple as this, if u observe you HAVE to disturb, there are no two ways about it.

One of the ways that the Heisenberg principle was explained to us in school was to take an atom and hypthetically observe it by shining a photon of light on it. You could then by purely theoretical arguements show that the Heisenberg Principle in its mathematical form would hold true.

Sending and recieving video is the part to be noted. For this you would need light, and when light is shone on atoms it changes their properties like momentum and energy. The Heisenberg principle would again come into the picture.

Al does not easily dissolve in cold concentrated acids such as sulphuric and nitric because of an oxide coating.......Mg will react with nitric acid in a jify....in fact even with extremely low concentrations

You can't ignore the most basic principle of quantum mechanics -- Heisenberg's Principle, i.e., the very nature of observation WILL change that which is being observed.....so I really don't see any of the encoding schemes working.