The second law of thermodynamic

[Bread_of_Life]

JLW

You can rant and rave all you want...

When have I ranted and raved? It seems to me that you havn't answered any of my substantive questions to you, preferring to say that I am ranting...?

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!

No, it's not.

LIM (x->infinity) 1/x -> 0, is an expression that fourier analysis (and any form of integration) is dependent on,).

That is not the same as saying that 1/infinity = 0.

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.

Have you answered the questions brought up by my link, or by myself?

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.

I hope I didn't claim this, I have a bachelors degree in Physics, not maths.

Do you recall the concept of limits?

Yup.

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

You used an equals sign. That's not correct notation. As n tends to infinity (n-> infinity), then 1/n tends to zero (1/n-> 0)

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

What I would like your enginerring mind to get itself around is some of the points I've made.

For example, if, as you claim, 1/infinity = 0, that would imply that:

Infinity x 0 = 1

This is clearly not true, no matter how many times you add zero to itself you never get 1. Let me put that in limit theory notation for you:

x1 + x2 + x3 ... + xn = Y

if all xn = 0

then

LIM (n-> infinity), x1 + x2 + x3.... = 0

In other words, the function defined by adding zeros again and again will always be zero, it does not tend to 1 in the limit. That would imply that

1/infinity /= 0

Could you answer this rather simple problem for me? Thanks.

[Bread_of_Life]

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?

because, in many cases Nebula, it doesn't really matter if it's 0 or dn. So, to make it simple for you in the majority of cases, it can be useful to think of it this way.

But nebula, think of this, what is division? What are we saying when we say:

10/2 = 5

What we're saying is that, if you take 2 fives, and add them, you get 10. So what are we saying when we take:

1/infinity = 0

We're saying if you take infinite zeros, add them all up, you get 1. Is this true Nebula? Say you took a jump zero metres long. Then another. Then another. Would you ever get anywhere? Would you ever get 1 metre? 1 centimetre? Does this arithmetic series add up to anything other than zero?

No. So 1/infinity /= 0. Sorry, it really is that simple, you can't divide a number by a concept and get a number back.

[JLW001]

OK, SA. This is where you part ways with every physicists that I have ever seen talk on this subject. Yes, infinity is a concept. However, Canton (from canton set fame) said that we can certainly perform some operations with infinity despite the fact that its a concept.

The fact is that the limit of 1/x as x tends to infinity (notice that it is x tending to infinity) IS zero. That limit is zero. You can't go anywhere else but to zero. Now, if I say, well infinity is just a concept, what does that mean? It means that the concept of infinity has no USE. I see the beauty of the logic that Canton used.

Now, I recall that you said the universe had infinite choices for its configuration:NOT the case if infinity is just a concept! If infinity is a concept, not a logical extension of real numbers, then you could say that the number of choices for the configuration of the universe tended toward infinity. There weren't infinitely many choices, but just tended toward an extremely large number.

SA, you can't have your cake and eat it too. If infinity is a concept, then don't apply it to anything with numbers, like infinitesimal probabilities. If you can allow yourself to see that limit theory shows that the concept of infinity is actually very useful, then were back to where your argument falls to pieces. Itis "either, or", not both. You can not prove anything with just the concept of infinity. You can describe things that aren't infinite and distinguish them from being infinite.

In mathematics, we can say that a function space is bounded or infinite. If its bounded then we can say what goes on about that space at that boundaries. What if its unbounded or infinite? We can still describe how functions will behave through the whole space and tell, in general what they will be doing along the "infinite" regions.

[JLW001]

SA, I decided to look at your link and am glad I did. Here's a quote from the good DR.'s response.

To go back to your chocolate bar, what if you divide it among every

person living on earth? Each person would get roughly 1 six-billionth

of a chocolate bar. That's a very, very small amount, and you'd

probably need a microscope to see your piece, but it wouldn't be zero,

right? Ah, but you asked about dividing it up amongst an infinite

number of people. Well, we can't. Why? Because infinity isn't a

number, so you can't show me an infinite number of people. If you try

to, I will just add one more person, and then we'd realize that the

number you thought was "infinity" actually wasn't.

Let's substitute "choices for configuration of the universe" for the chocolate bar. You will never have infintely many choices because infinity isn't a number! And if there aren't infinitely many choices what does that mean? It means that something or, dare I say someone, limited how many configurations there would be. Or, in other terms, the big bang was not the first cause. Or, God said there is one choice for the universe and this is it.

[JLW001]

I thought I would mention the following in response to this quote.

What I would like your enginerring mind to get itself around is some of the points I've made.

For example, if, as you claim, 1/infinity = 0, that would imply that:

Infinity x 0 = 1

This is clearly not true, no matter how many times you add zero to itself you never get 1. Let me put that in limit theory notation for you:

x1 + x2 + x3 ... + xn = Y

if all xn = 0

then

LIM (n-> infinity), x1 + x2 + x3.... = 0

In other words, the function defined by adding zeros again and again will always be zero, it does not tend to 1 in the limit. That would imply that

1/infinity /= 0

Could you answer this rather simple problem for me? Thanks.

You are posing what's known as the "indeterminant form". You see Canton showed that infinity could actually be treated as a type of number, like real, imaginary, etc. Then those operations I listed above apply.

[JLW001]

I thought I would summarize...

1.) Infinity is a concept...an idea. This means saying I have infinite raisins, infinite chocolate bars or infinite choices is wrong. It can not be. Because infinity is always one step ahead of us. Imagine that!

This is as far as some mathematicians wish to take the idea. However, they do not balk at all with using zero, despite the problems with indeterminant forms that arise with zero. There is a deep link between nothing and infinity.

2.) There are some logical conclusions we can make by evaluating the impact of infinity. This means that just as counting numbers, integers, real, and imaginary are types or sets of numbers that have certain rules of operation associated with them, I can make a new set of numbers and the set contains infinity and that's it.

So, how do I start showing what operations I can do with infinity? Why, with limit theory. Limit theory says, "What happens to an expression when some part of that expression approaches a number?". I could say what is the limit of the expression, "2X", when the variable "X" approaches 1. OR

LIM (X->1) (2X) = 2

That limit says that the expression goes to the value of 2 when "X" goes to 1.

Now, can we use limit theory to tell us what certain expressions are when a number toward infinity? YES.

LIM(X->inf) (2X) = inf

It doesn't matter if I double or triple or quadruple infinity, because infinity is always at least 1 more. Always one more. That is profound once you grasp the logic of limit theory and infinity. We can do things with a concept that is not physical in meaning. That has the likeness to having a small window into things that are not in the physical. God even provides a way to look beyond the physical in a "physical" sort of way. Profound indeed!

Using limit theory and Canton's logic we can provide a list of allowable operations for our set of numbers we call infinite. In fact you might say that zero has similar properties as infinity. We can't imagine dividing something into nothing. Yet, we certainly understand the other operations like adding, subtracting, and multiplying by nothing. Yet, most mathematicians readily accept the concept of zero. However, if we logically examine what it means to divide something by nothing in a limit theory perspective, it defines the link between the other sets of numbers (real, integer, counting, etc) and infinity.

LIM(X->0) (2/X) =inf

As "X" gets smaller and smaller, the effect of dividing it into the sets of real, integer etc. becomes a rapid increase of value that is not bounded. That is, by definition, infinity.

We can also see that...

LIM(X->inf) (2/X) = 0

This means that as "X" increases without bound the effect of dividing it into a number is to go toward zero. That means that "2/X" keeps getting smaller and smaller as "X" keeps getting bigger and bigger. This means the limit of the expression goes to zero. It will never go anywhere else. And by using Canton's logic we can see that 1/inf is in fact zero.

Now, the trouble comes where you have the state of inf/inf. This is indeterminant as defined by Canton. If we have expressions like (X/X) then, we have...

LIM(X->inf) (X/X) = undefined.

In order to evaluate that limit we can use L'Hopital's rule. L'Hopital's rule (LR) states that the limit actually depends upon how fast the numerator is going toward infinity compared to the denominator. Now, when ever we are talking about "how fast" or rate we need to use calculus. For simplicity's sake I will give a quick definition of how to calculate the rate or diferentiation of an expression. This is the quick and dirty of it by example.... d(expression)/dX means the rate with respect to X

d(X)/dX = 1, d(X^2)/dX = 2X, d(X^3)/dX = 3X^2 and so on...

Now, applying L'Hopital's rule...

LIM(X->inf) (X/X) = LIM(X->inf) ((d(X)/dX) quantity divided by d(X)/dX)...

substituting d(X)/dx = 1, we get

LIM(X->inf) (X/X) = LIM(X->inf) (1/1) = 1, excellent!

Now, if I apply it to the case of...

LIM(X->inf) (X^2)/(X) = 2X = inf

and so on... here's a decent link for a tutorial...

http://www.math.hmc.edu/calculus/tutorials/lhopital/

So, there are indeterminant forms when using infinity in calculations, but as long as we use sound principles and good math, then it is very easy to utilize the concept of infinity to solve problems.

Infinity is a concept that is very useful. It allows us to have a sneak peek into things that otherwise would be lost to us. However, we do encounter indeterimant forms with infinity, just as we have with zero. However, both are extremely useful for understanding our world.

Edited March 10, 2005 by JLW001

[nebula]

BTW - what was the discussion that the "infinity" argument sprang out of?

I tried re-reading stuff and got lost.

[JLW001]

We started this by discussing the first cause of the universe. SA claimed that the principle of Occam's Razor showed that God was an unnecessary object. He said the first cause was the big bang or equivalent. By first cause, we mean the beginner that had no cause and is therefore not an effect of something else. Occam's razor is a principle that says if I multiply all the probabilities for things that I am uncertain of in my theory1 and I do the same for theory2, then whichever answer is the highest is most likely the "most true" theory. Now, adding God in front of the big bang has no effect except to extend the number of objects in the theory, it does not say what the product of all the uncertain object's probabilities will be.

I pointed out that there are so many objects in the universe that have extremely low probabilities of occurrence if there is no designer. DNA for example. This shows that the Occam's razor multiplication result for a random universe goes to zero very quickly and that a theory that includes a designer (God) has a multiplication result that is not zero.

Then we kind of had an aside about conditional probabilities, but Occam's razor requires the use of unconditional probabilities.

Then SA, said that if the universe had infinite choices of its state, then there's a chance that all of the necessary, but extremely low probability (if looked at as random) occurences could have lined up just by chance. Then I promply showed that if you have infinite choices or lottery balls or whatever, then you will never pull a lottery ball or have a universe chosen because the probability of each of the infinite choices is zero or 1/infinity.

SA then quickly stated that you can not divide by infinity because it is a concept and not a number. I argued that you could and should use it in this instance because the result was not an indeterminant form, like inf/inf. Then we have come to the point that we are now.

You can't have infinite choices for a random universe if infinity is not a number. You can have infinite choices and, very important, a non-random probability distribution. Then you simply have those choices that are preferred and the rest are zero. However, as soon as you say that you have infinite choices and that each choice is equivalent inprobability, the the probability becomes zero.

Now, where is all this going? If you have preferred states for the beginning of the universe, then something told the big bang what those preferred states are and thus, the big bang is not the first cause.

All this exercise is showing is that if you pursue truth in the universe you will find God in every circumstance. God is in the infinitely small volume at the center of a black hole and He is in the balance of star ages in the universe (so that elements like C, O, H, N, Fe, Ca etc. will form but not be destroyed in the stars). He is in the location of our sun relative to the galaxy core and in the perfect distance the earth is from the sun. He inhabits infinity and He comes from nothing. He is the first cause and the last, the Alpha and Omega.

I'm not sure why SA resists this so much. I think he's smart enough to understand and get these concepts, but he seems to be unwilling to admit that God exists. Most every scientist of note in our recent history knew God existed and trusted in Him. The true study of the universe leads one to the conclusion that God exists. It says in the Bible that the creation declares His glory...and thereby His existence.

[nebula]

Thanks, Jamie!

Of course, I do wonder how the Big Bang can be considered "first cause" - as if the Big Bang was an entity and not the result of something!

[JLW001]

SA, you seem to have forgotten to respond as to why infinity is a concept and not a number but that you can still use it as a number...but only for your argument and no one elses.

I'm sorry, but its really hard to take you seriously sometimes. You're quite good at dropping big words and changing subjects when things seem to be going "not so well" for your denial of God. However, you have not convinced me scientifically that any of your arguments in this thread hold any water. As a matter of fact I have given you good solid evidence in why you should believe in God or at least some higher power. The universe is not some cosmic accident. You can not justify any thought like that because the mathematics of it are wrong. Occam's razor shows that believing in the "theory" of God is much more scientifically sound than in believing in random generation of what we see.

Oh, one more thing. Every living creature does have a common ancestor. I know, I know it's been something that I've finally understood about evolution.. There I have admitted it. We have a common ancestor with sea algae...........................................................................

...........................................................................

GOD!