The second law of thermodynamic

[JLW001]

You made this statement regarding 1/infinity.

We cannot evaluate the expression. Infinity isn't a number, so we can't come up with a numerical answer. In fact, what we are talking about is having an infinite set of balls, each with an equal but infinitessimal probability of occurence. Infinitessimalness does not equal zero, it is the next smallest thing, dn if you will.

Wow! SA, I'm dissapointed in you bud. Check your precalc or Calculus book or for that matter most good algebra books.

One divided by infinity is zero !

I wanted to write that out so there was no mistake about what my notation was. We can calculate division of a real number by infinity and we can calculate the multiplication of a real number and infinity. What becomes indeterminant is the division of infinity by infinity.

I can try to find a link for you to a good math website if you'd like.

[JLW001]

Do you now see why its called the gambler's fallacy.

If you say "well not infinity, but just a big number," then I can say why were the choices limited and we're back to God. You can't get around it.

As soon as you say uniform distribution and infinite choices, then you reach the Gambler's fallacy, because 1/infinity = 0. Now, you could say infinite choices, but a non-uniform distribution, then we're back to reality.

Now, what I'm showing you should be enough for you to say, well maybe there is something to this God thing. I hope that you see this. I did not undertake this as a match of intellects or knowledge, but as achance to show you that what you have been taught to prove that God doesn't exists simply proves his existence. As long as the scientist remains objective and is truly seeking the truth, then it will always lead to God.

[JLW001]

Also, you don't seem to have answered by question about throwing a dart across a room. Since space is a continuous variable, if I measure the position of a point on my dart in a metres time, there are infinitely many points and infinite possible positions I could measure. Yet I only measure one. How is this possible if each has a probability equivalent to zero (given a random throw).

Ahhh. Now we get to the quick of it. Measurement does not involve probability distribution until you get to quantum level and even then you have a determinant probability distribution.

To be honest I don't even remember your setup of this problem so I'll speak to what I think you are talking about. Its all summed up in this.

There can be infinitely many choices as long as there is a determinant probability distribution. If you say each infinite point has the same probability then we get to the indeterminant form and an indeterminant probability distribution.

[Bread_of_Life]

http://mathforum.org/library/drmath/view/62486.html

Notice btw, I didn't actually look this up prior to posting my stuff about 1/infinity. It's just a mathematical fact I knew from having studied maths at a higher level. You can't divide by infinity, because it's not a number.

Oops, looks like it's you we should be disappointed in

[Bread_of_Life]

By the way JLW, where do you get off telling people they're wrong when they're not, and that you're disappointed in them? I take it you must be well studied in maths? Graduate level?

As you can tell, being right makes me happy )))

[JLW001]

Look, SA. I don't need to justify any of my cognitive ability to you, but I will so that others who read this can see.

I have a Masters of Science Degree in Chemical Engineering. I completed my Thesis on Least Squares Finite Element Methods for solving the Navier-Stokes Equations. That's computational fluid dynamics. I have written hundreds of pages of computer code in Fortran77 for the numerical solution of these flow equations in applications for open boudary conditions for water flow as well as modeling the dispersion of pollutants in the atmosphere using turbulent models with 31 chemical reactions that involved stiff-systems of ODEs (that's ordinary differential equations) in the chemistry. I have published three papers, journal articles, in peer reviewed journals of good reputation. I have made a good breakthrough

in the thermo-capillary flow involved in molten metals. That is the paper I am most proud of. It was publish in the Journal of Heat and Mass Transfer.

I left school with my Masters but was only a year away from my doctorate. I left because of the birth of my son.

Now, I have completed four semesters of calculus. I have completed graduate classes in mathematics all the way to Fourier solutions for Partial Differential equations. That includes matrix algebra, advanced calculus, two symesters of functional analysis, and advanced solutions of large sparse matrices that result from complex systems.

Let's see. Let me demonstrate to you the idea behind why we can use infinity in arithematic operations.

1*inf = inf

2*inf= inf

..

..

inf*inf =inf

There's the multiplication.

Now, the division....

1/inf = 0

2/inf = 0

.....

inf/inf = INDETERMINANT FORM

Now, that's the life of infinity in our arithmetic. Let me link you to a site that describes this so that you don't just have to take my word for it. If you have indeed taken graduate level mathematics or indeed high school advanced math, then you would know these mathematical properties of infinity. Now its just a question of whether you will admit it.

Let me demostrate why we can divide any real number by infinity...

let's start with easy fractions that most every one is familiar with.

1/2 = 0.5

1/3= 0.33333....

1/4 = 0.25

1/5 = 0.2

...

1/100 = 0.01

...

1/1000= 0.001

...

1/10,000= 0.0001

Now, we can see that as the denominator get's larger the fraction actually get's smaller. Now, how small can the value of that fraction become....it will never reach zero as long as we use real numbers. But what if....

Let's imagine that the bottom of the fraction becomes larger than any number, that's infinity.

1/inf = 0.

nuff' said.

Btw, here's your link to the arithmatical properties of infinity.

http://mathforum.org/dr.math/faq/faq.divideby0.html

If you scroll down the page you get to see all of the arithmatic properties of infinity. It looks like this....

infinity + r = r + infinity = infinity

(-infinity) + r = r + (-infinity) = -infinity

infinity + infinity = infinity

(-infinity) + (-infinity) = -infinity

infinity - r = infinity

(-infinity) - r = -infinity

r - infinity = -infinity

r - (-infinity) = infinity

infinity - (-infinity) = infinity

(-infinity) - infinity = -infinity

infinity * r = r * infinity = infinity for r > 0

(-infinity) * r = r * (-infinity) = -infinity for r > 0

infinity * r = r * infinity = -infinity for r < 0

(-infinity) * r = r * (-infinity) = infinity for r < 0

infinity * infinity = (-infinity) * (-infinity) = infinity

infinity * (-infinity) = (-infinity) * infinity = -infinity

infinity / r = infinity for r > 0

(-infinity) / r = -infinity for r > 0

infinity / r = -infinity for r < 0

(-infinity) / r = infinity for r < 0

r / infinity = 0

r / (-infinity) = 0

SA, I take no gloating over this. Even though you have reacted in quite a sarcastic, if not mean, way. I know that you will probably never admit on this thread that you are wrong about the value of 1/inf, but I know in your heart that you do know the truth. May God lead you to his peace. I will only glorify my God for having shown this truth to you and hope that he leads you to himself.

Edited March 9, 2005 by JLW001

[JLW001]

I'm sorry, I mis-stated the journal for my thermocapillary work. It was Numerical Methods in Heat and Mass Transfer.

[Bread_of_Life]

I have a Masters of Science Degree in Chemical Engineering.

Yup. I thought you'd be an engineer.

Navier-Stokes Equations

Uuuuh, that had to be one of my least favourite partial differential equations.

I left school with my Masters but was only a year away from my doctorate. I left because of the birth of my son.

Ooooh, that's sweet (still, tut tut, education first!). What's the wee lad's name, how old is he now?

Now, I have completed four semesters of calculus. I have completed graduate classes in mathematics all the way to Fourier solutions for Partial Differential equations.

You know, I almost fell asleep when I was learning about Fourier analysis - it only really came to life when I was learning Biophyics of Nerve Cells and Networks, and found out that fourier could be used in the analysis of synaptic noise.

However, back to topic. I don't see how any of the above qualfies you in the theory of maths. For example, I don't see how any mathematician could seriously write:

1*inf = inf

2*inf= inf

Clearly this proves that infinity cannot be multiplied, that it is a concept not a number.

1/inf = 0

2/inf = 0

I'm sorry mate, you're still wrong. Ask any theoretical mathematician, you cannot divide by a concept, only by a number. 1/infinity is formally meaningless. I'm sorry dude, it's just true.

Now, that's the life of infinity in our arithmetic.

No, it's not, and no solution to the Navier-Stokes equation is going to change my mind on that.

Let's imagine that the bottom of the fraction becomes larger than any number, that's infinity.

1/inf = 0.

Sorry mate, your example doesn't prove anything, other than that 1/bigger and bigger numbers tends to zero. But it doesn't reach it.

Infinity is a concept, it doesn't really exist quantifiably. Let me try to explain again:

There are infinite real numbers between 1 and 0. Question: How much are each of these real numbers seperated by, what is the seperation between them?

Answer: 1/inifinity

But hang on, if 1/infinity = 0, then each of these numbers must be the same. That can't be right.

I'm sorry mate, you have just about the understanding of theoretical maths that I would expect from an engineer. I'll bet you can deal with partial differentials very well, and even vector calculus. And I bet you can eat thermodynaics and Enthalpy for breakfast. But here, you're in the field of theoretical maths, and you really don't know what you're talking about. Sorry dude.

http://mathforum.org/dr.math/faq/faq.divideby0.html

Well, there we are, mathforum contradicted itself. Frankly, I'm not too bothered, go ask a theoretical mathematician, infinity is a concept, not a number - it cannot be evaluated, and therefore cannot be used in ordinary algebra without "weird" consequences.

Actually, I left one of those "weird" consequences out here. Maybe chewing this over will help:

1/infinity = 0

therefore

Infinity x 0 = 1

therefore

0 + 0 + 0 ...... ad infinitum = 1

We know, a priori, that this cannot be true. No matter how many times we add up zero we will always get zero. We will never get closer to 1, not even a single iota closer. We will never even get to dn. This cannot therefore be true.

Think of the chocolate bar in the example I linked you into. What if you broke that 1 choco bar into infinite piece. If each piece weighed zero grams, what happened to the chocolate bar? Zero+Zero = Zero, zero means "non-existant". If you add up even infinite parts of non-existence, you still get non-existence.

Is this starting to make sense now?

Also, by the way, have you noticed that the article you linked to is self contradictory? It says "don't divide by 0".

Yet, if:

1/inf = 0

then

1/0 = inf

1/0 is undefined, you can't do it. Oops. Sorry man, you're going to have to go back to the drawing board on this one.

SA, I take no gloating over this. Even though you have reacted in quite a sarcastic, if not mean, way.

Yup, and you were being patronising, even though you were incorrect.

[JLW001]

SA, I don't know what to say. I'm at a loss.

You can rant and rave all you want...but 1/inf=0 Let me see how many other links I can post to show you that...but first, You have no idea about fourier analysis if you don't think that 1/inf=0. Do you know why? Because that's one of the concepts that makes Fourier analysis work!

Let me link you to several other sites that do indeed show the same thing that mathforum.org shows. I thought it would be quite nice to show you the truth from the same site that you thought to deceive with.

Btw, which link on mathforum.org is incorrect? Neither. Infinity is not a counting number. But you and others who read this will indeed see that we can still use it to some extent. Namely, those properties I listed from mathforum.org.

Now, let me demonstrate to your great mathematical mind (btw I noticed in another thread that you claimed a bachelors degree in math, was that bachelors of arts or science) in more concrete terms.

Do you recall the concept of limits? Right now lets look at the algebraic function,

Y = 1/(2*n)

Let's draw a graph of Y verses n....or in this case a list of numbers

if n=1, y=0.5 if n=2 and so on and on.

Now where does that graph stop, SA? It doesn't. OK, then how can I know what number the value of "Y" approaches for really big numbers of "n". Why, let's use limit theory! Good idea. You do remember limit theory don't you, SA? OK...let's use the limit as n=10^100. So, we plug and chug and get Y=5x10^-101. That's scientific notation in case you wanted to know. It represents a decimal point with one hundred zeros to the left of it and the the 5. No, that's not a big enough "n". I'm mean really big! How about the biggest! INFINITY. Yaaay! Now we get to use our limit theory.

if we say what is the limit on the value of Y as n gets larger and larger and goes to infinity.

in limit theory notation (as adapted to text)...

LIM (1/(2*n)) = are you ready! ...........................ZERO.

n->inf

Now, if that is too much for your great mathematical mind (as opposed to me alowly engineer )to get, SA, then I'm sorry.

BUT, you don't have to take my word for it......................

http://tutorial.math.lamar.edu/AllBrowsers...sOfInfinity.asp

http://www.newton.dep.anl.gov/askasci/math99/math99008.htm

http://whatis.techtarget.com/definition/0,...i809150,00.html

http://www.jimloy.com/algebra/two.htm

http://mathworld.wolfram.com/Infinity.html

I've got to go, but I'll have more links later on.

[nebula]

I left school with my Masters but was only a year away from my doctorate. I left because of the birth of my son.

Ooooh, that's sweet (still, tut tut, education first!).

I seriously hope you were being sarcastic here.

For example, I don't see how any mathematician could seriously write:

1*inf = inf

2*inf= inf

Clearly this proves that infinity cannot be multiplied, that it is a concept not a number.

If this is impossible to do, then why in Calculus class are we taught when you divide by an incredibly large number, the result is 0?

When a graph shoots off to infinity in the negative direction (for either the x or the y axis - or in the z as well, if applicable) - which dividing does - it becomes 0.

Example in the physical:

If you are traveling from Point A to Point B in half incriments, via algebraics, you will never get to point B, for there will always be a "half" point between where you are and where point B is.

But, in real life, ther comes a point where the "half-way" principle is superceded by practicality - 1/2 of two steps is one step - and after that no one will take a "half-step" for an infinate number of steps. The person merely, takes the final step to point B. As one approached "infinity" in the negative direction, there comes a time where 0.00000000000 . . . 0000000001 becomes pointless, and you supercede all the infinite zeros and just take it to zero.