Recent content by Manny46

I agree completely. Both of these processes have their own place. While intuition, induction and empirical evidences are useful for forming conjectures, but it can't really be established as a theorem without deduction. Thanks for that trivia. Makes me more interested in the history of...

Special thanks to fresh_42 and also sysprog for their valuable insights. While it's not entirely possible to know the exact process, but I think this extract from Foundations and Fundamental Concepts of Mathematics by Howard Eves does a great job of clarifying it. This is not to say that the...

I see. Thanks

Thank you so much for your insight.I guess, the only way to get hang of this process is to read and do more math. I have just started doing real analysis, what do I know yet.

I'm missing something here, would you elaborate on this point? What I get from here is that mathematicians build up from the previous works and results of other mathematicians/their own work.

Thanks for clearing that up. So the key point is, that we understand the concept, the idea behind the theory rather than cooking up new theorems by just maneuvering axioms/theorems. I mean it does involve the latter but at It's core It's a creative process where one needs to fully grasp the...

Is it something which proceeds like a follow-up/deduced from one proposition to another? Or is it something where one forms a conjecture, convinces himself of its truth, and thereafter tries to prove it deductively? Do you have any recommendation for a book on Euclid with creative process as its...

What I basically want to ask here is, about the process of forming mathematical truth/theorem. This seems like a bit broad question, but I have this specific query. We all know that Euclid started with his basic postulates or what we may call axioms, and common notions. Now did he form those...

Yeah that helps, basically if there's a friction and when the train stops accelerating it becomes an inertial frame where Newton's laws work. Now that due to train's acceleration, puck acquired some velocity backwards (if train moves forward) and now due to friction it comes to rest (w.r.t...

Here I definitely assume some engine working on it in a very controlled manner. Like, let's say a car which accelerates from 0 to 60 mph in some seconds, and then it stays at 60. Something to that effect. Though got your point.

Oh I apologize for not being precise enough, but I get your point. Thanks

I mean without going for the numerical details, my question is w.r.t. board achieving a constant speed (of course board is long enough, less friction here), will the puck keeps moving backward when the board moves forward at a constant speed or it goes along with it with the same speed?

Now here's the thing, board is large enough, less friction and board comes to a constant speed, what happens then? Also if the friction is large enough, won't puck stay where it is?

I'm not being extremely exact here, but suppose there's a puck in a board where there's very little friction. Both puck and board are at rest. Suppose the board starts from rest to some decent speed, so there's definitely this acceleration, by virtue of which (and also less friction), puck...

Well, when puts Einstein in the frame, it automatically makes it non inertial. I just checked, you're correct, Sir. Volume 1 ( which includes Krane ) has Resnick/Halliday/Krane and Volume 2 has (Halliday/Resnick/Krane).