Exploring Limit Laws with Infinitesimals

[sutupidmath]

Have a look!

Hi all,

Well, i am posting the work that i have done in proving that theorem. Like i said it is nothing important, but rather it is important only for me, so if you could have a look at what i have done i would really appreciate it.

The theorem that i have tried to prove differently is the theorem upon the limit laws. I already know how to prove limit laws using Cauchy's definition of limits, and also using Heine's definition(that is in terms of sequences), but the way i tried to prove them is using only and only infinitesimals. In other words, i first tried to prove some properties of infinitesimals, as a background information, based solely on the definition of infinitesimals. I also have never seen the properties of infinitesimals proven solely on its definition,but rather based on the properties of limits, so if you could pay heed to that part too i would appreciate it.

The main point here is the theorem upon the Limit Laws. If someone of you could spare a few minutes and let me know if i have done anything at all, i would really appreciate it.


Thanx in advance

P.S. I am going to upload the file in two pieces, since it seems to exceed the capacity of uploading here.

 

[sutupidmath]

Well, i probbably shouldn't have uploaded in .doc thing, but i just don't know how to convert it to pdf or sth.

 

[Darkiekurdo]

Well, i probbably shouldn't have uploaded in .doc thing, but i just don't know how to convert it to pdf or sth.

You can convert your files on http://media-convert.com/

Or alternatively, if you're using OpenOffice, you can go to 'File -> export as PDF'

 

[bravernix]

I like this little app because it installs like a printer (so you just print to it and out pops a PDF).

http://www.cutepdf.com/Products/CutePDF/writer.asp

 

[sutupidmath]

Ok, i tried to convert them here, they are on a pdf format now. If you could have a look at it, i would appreciate it. It is in two parts, because i could not upload it as a whole.

Any comments so far?

 

[sutupidmath]

Hey Guys, don't hesitate to tell me on the face that i haven't done anything at all. That won't hurt my feelings at all. I have had enough joy while doing what i did, so now i only like to have some comments from a completely objective and realistic point of view.

Thanx in advance!

 

[sutupidmath]

HOw come all these views, and no comments at all?

 

[mgiddy911]

Give it some time. Please do not demand comments and suggestions from people here.

 

[Vanadium 50]

First, we're not a bunch of trained seals. You're asking people to spend some of their time looking over your work. A little less of a demanding attitude would go along way. Maybe even a wee bit of gratitude would help.

Second, this thread title is just about the least descriptive one possible. Only "Help" is substantially worse. If you aren't willing to spend a minute writing something descriptive, why should we be willing to spend 20 minutes investigating your proof? Is your time really 20 times more valuable than ours?

Third, your question has been asked and answered in another thread (titled, equally generically as "Advice needed!"). Cyrus said, "There is a reason why he said it could be proven that way, it has been proven that way. You are simply rehashing a known result, there is nothing worth publishing. Sorry." Asking again on another thread is unlikely to get you an answer you'd rather hear.

You've learned something by proving it in a different way than you've seen before. That's good. Accept it, without trying to make it more than it is.

 

[sutupidmath]

Second, this thread title is just about the least descriptive one possible. Only "Help" is substantially worse. If you aren't willing to spend a minute writing something descriptive, why should we be willing to spend 20 minutes investigating your proof?

You've learned something by proving it in a different way than you've seen before. That's good. Accept it, without trying to make it more than it is.

Well, thankyou for your comment. Well, i have already decided a couple of days ago not to even try publish it. I realized it is not worth. So, actually the purporse of this thread is far away from hearing what i actually would llike to hear a couple of days ago, but now that story is over.
The reason that i posted what i did, is that after i checked my work with my professor, i had a feeling that the prof. did not pay that much attention to it, for the reaon that he/she just glanced over it, and also there were some two or three mistakes in there that she did not even notice, i fixed those mistakes later, when i proofread it. So, i started to suspect that there might be a lot others, or even that those proofs arent at all consistent.

First, we're not a bunch of trained seals. .

I am completely aware of this. Moreover this would be the least thing i would think for the people in this forum, who take their time to enlighten our ingnorance.

You're asking people to spend some of their time looking over your work. A little less of a demanding attitude would go along way. Maybe even a wee bit of gratitude would help..

I agree, i acted a little bit in a rather silly manner, because i know that nobody out there is obligated to check our work, or help any of us. I appologize for that.
On the other hand, although it may not look so, i really appreciate and gratitude the work that any of you out there do for the people here, maybe more than you could even imagine. It just that sometimes we lack reason when we really want sth.

Is your time really 20 times more valuable than ours?..

No not at all. I really think that many of you might be way way busier than i am.

Third, your question has been asked and answered in another thread (titled, equally generically as "Advice needed!"). Cyrus said, "There is a reason why he said it could be proven that way, it has been proven that way. You are simply rehashing a known result, there is nothing worth publishing. Sorry." Asking again on another thread is unlikely to get you an answer you'd rather hear. ..

Yeah, i know. But like i said the purporse of this thread is no more to get the "green light" for publishing it, instead i now just want to know whether what i did there is mathematically right.


I really thank all of you. There is no concrete means of expressing my gratitude to all of you out there, but trying to help others the way some of you do help us, what other means could there be?