They will be greater in the example I gave you. I am disappointed that you did not understand this. There are no negative numbers in the series, so you are just confusing matters. Truth to tell, you have no grounding in basic mathematics. What you need is to enrol in a suitable course rather than confuse yourself playing about with concepts which you clearly do not understand.
\( \frac{1}{\omega_{n-1}}\int_{S^n}\langle 1 | e^{sH} | 2\rangle \, \mathrm{d}\Omega = 3 \times \infty \) And so we can prove infinitesimal x infinite = infinite, modulo the category of fibre bundles, obviously.
Myles, you are quite mistaken that I have no grounding in mathematics. In college, I studied up to Calc 3, and I also had three semesters as a physics major. Please cease to belittle my intelligence friend. I am also a licensed professional attorney, and have dealth with many very complicated legal theories which would make your head swim. And trust me, I know you did not answer my question. So, would you please attempt to do so.
What Guest254 said is his way of telling you that you've got no clue what you're talking about. Calc 3 is a good start, but it won't give you a proper understanding of what infinity means mathematically. You need to take a course in analysis, that's where you learn these concepts in a rigorous, detailed setting, and it will clear up all your confusion.
Hehe, it seems to me the number of threads people post here destined for the pseudoscience section vastly outnumber the number of threads people make asking legitimate mathematical questions. And it seems the rate at which these threads get sent to the pseudoscience section is inversely proportional to the background knowledge of the original poster.
It's called taunting. He's saying that what you write is a load of gibberish, and then he posted some gibberish as an example of what he's talking about.
Anyhow if you want everything explained in plain English, I'm afraid this isn't the place for it. You're trying to discuss the mathematical concept of infinity in a way people with next to no background can understand, and this isn't possible to do any more than it's possible to explain calculus to a layman without having them learn the background first. You need to take some analysis courses or pick up an introductory text in mathematical analysis, learn what mathematicians mean when they say "infinity" or "infinitesimally small", and once you've done that, then you can come discuss this in a scientific setting. Otherwise, what you're doing is akin to a person who speaks only Mandarin trying to study the works of Shakespeare.
As a lawyer, I know for a fact that scientists are quite capable of making complicated subjects accessible to the layperson, because they have to in order for a jury to understand what they are saying. I've met many scientific folks who are quite capable of this feat. If you are not, than just say so. That doesn't mean you're right, however. The inability to explain a complex subject at a grass roots level is not proof that you must know what you are talking about. If anything, it's proof that you don't know what you're talking about, otherwise you could explain it. The ability to explain complicated subjects to the layman is a true test of your own knowledge. Now, I am not even a layman. If you can't explain it to me, you would have little hope in front of a true layman.
I am not belittling your intelligence.; it's your knowledge I am questioning. You clearly do not understand the definition of infinity or you would have understood what everyone here has been telling you. Lawer or not , you are thoroughly confused on this one. Perhaps you also majored in arguing. Well, count me out. You clearly do not want to understand as despite being refuted a number of times, you continue to repeat yourself to no good effect. Put simply, you are up the creek without a paddle.
At the risk of being offensive by breaking in, may I point out that explanation is a two-way process. The explamation must be clear but it will fail to convince if there is no background knowledge or intelligence to grasp its meaning. There is a limit to what one can do in this respect. Try explaining evolution to a fundie or, in this case, a mathematical concept to someone like yourself. You have made your mind up so you will only listen to what you want to hear. The jury will take note of that last remark. I find it impossible to believe that you took calculus , yet managed to avoid learning about limits, infinity and so on.
I'm not sure what is meant by calc 3 but I can say that one of my earliest lessons in calculus covered limits and infinity Simple differentiation includes the idea of a value tending to 0.
When has anyone ever needed to explain the mathematical definition of infinity or an infinite series to a jury? These are abstract concepts, and yes I could explain it to you, as a layman, but why spend all that time when you can look it up in a book, and I could always refer you to good sources? When a scientist comes in to explain the subject of DNA testing, do you think they're going to lecture the jury about the structure of DNA and the properties of molecules, chemical reactions, quantum physics and the periodic table, and everything down to precise detail? I can't teach this stuff to you based on what you already know, because there's a great deal of background knowledge you need to learn first. I have tried to explain infinity to you, but it's clear you struggle to understand the explanations because you keep jumping the gun. You're asking questions that are answered by the subject of mathematical analysis, and anything I could teach you about this subject you can learn in more detail from a proper textbook. Besides, if I were with you in person it would be way easier than typing out dozens of pages of math here on the internet, that's a lot of work to do just to answer a question that really doesn't have any mathematical merit.
Calc 3 as I learned it also covered these subjects, limits and infinity, and so on, but we never learned it in proper detail to rigorously answer the questions being posed here. That's why John is having all this confusion in the first place- there's a reason we have courses titled "Analysis", it's precisely to deal with these kinds of topics.
Things have changed since my day, almost sixty years ago. I remember a textbook with "infinitesimal calculus " in the title. Something tells me that goes back to Newton and Leibniz.
Here is how i see it. An infinity is a number which is found to increase. Naturally, as we call them an increasing integer that can be positive or negative. My questions stems from this, in where we mark a boundary on an infinity? For instance, you can have one infinity, by mathematical logic, and yet still have another infinity when deducted leaves a finite remainder, depending on those who still hold to the logic that the remainder is undefined, whilst it is, but this is because we can never have a true lay-out or blueprint if you wish of any exact value of any infinity. Not unless we can know what happened in the past and the future simultaneously... This would render any chaotic system from disturbing the theory we end up with.
Yeah, "infinitesimal calculus" usually refers to the early days of calculus, when the seeming paradoxes about infinities and infinitesimals had yet to be resolved. Back in those days, the kinds of questions asked in this thread would have been perfectly legit, and noone would have been able to provide a good answer. But of course as we know, in the mid-1800's with the invention of analysis, calculus was put on a rigorous footing and all of these paradoxes were easily resolved.
OMG - you know about chaos theory too! Is there anything you haven't studied!?!?! Please Register or Log in to view the hidden image!