Recent content by QuantumQuest

What I mean is: up to the point where we have no means whatsoever to count further.

Fair enough. Although I just try to give an abstract idea - I have already mentioned in post #27 I think that I did it in a rather violating way regarding math lingo (referring also to post #28 by @jbriggs444). So, I apologize for it. What I essentially mean is that our counting goes till very...

Well, my main argument is in the first paragraph of post #27. Now, in the second paragraph, I try to convey some ideas in an essentially informal manner. You are right that the word "the" you've highlighted carries an assertion of existence and uniqueness which, obviously enough, cannot be...

@dakiprae This is no kind of aggressive comment but I think that you keep on mixing the notion of infinity with the ordering in natural numbers and going from the first to the second in a somewhat alternate and arbitrary manner, during the same line of thought. As has already been pointed out...

I would recommend downloading MySQL Workbench, if you have not already done so. There, you can first design an E-R Model - you can do it in small steps as you are a beginner, by examining what entities you need and the relationships between them. This way, you can create a model with no...

If I understand it correctly, the claim is that unless something completely untrue - at least based on our current knowledge and experience, is stated, the discussion about the what-ifs of history must be distinguished from personal theories / speculations. In my opinion, it is not that clear...

Yes, I agree. This was a more general comment - that's why I have it in a separate paragraph, but unfortunately - according to my experience, it is absolutely true. It's true that I wouldn't do it for a small system like the one that OP is referring to but the fact that web hosts don't support...

As a web developer, I can assure you that if I had to create the whole thing from scratch, I would definitely go with PHP and MySQL (or MariaDB). Not because these are a part of the main technologies I work with but because they are open technologies and a great fit for anything small to medium...

My question is, have you studied the pseudocode for this? I ask because, the way you write it, seems that you're trying to understand it somewhat in the abstract. This is not necessarily wrong but studying the pseudocode of an algorithm is helpful in any case and particularly when you have any...

@Adesh I think that after my explanations in post #130 things are sufficiently clear. What you see in Fig.1. is the surface of a table. Now, you see the two handles beneath the surface of the table. These are used to pull an internal movable surface - as I said in post #130 you can think of it...

(corrected "interval" you had in your quote) Internal means inside, in the interior of something. Now, if you read the second phrase right after the first one it's easy to see that there is an internal surface inside table that can be pulled outside by using two small handles. To explain even...

As the Question ##6## is already solved I find it advisable to post my own solution as well. Let's take the function ##f: (0,+\infty) \rightarrow \mathbb{R}## with ##f(x) = \ln{x}##. We have: ##f'(x) = \frac{1}{x}## and ##f''(x) = -\frac{1}{x^2} \lt 0 \hspace{0.5cm} \forall x \in (0,+\infty)##...

Well, I was given this exercise as an undergrad some decades ago just like I'm giving it in this challenge thread - i.e, no modifications. While there are of course the cases you mention, the question is looking for the general case where ##a_1 \neq a_2## and ##m_1, m_2 \neq 0##.

Yes, I see what you mean but in order for other people to understand it, I think that it is best to show how to utilize the derivatives and the appropriate theorem in order to reach the point where ##\ln (m_1 a_1 + m_2 a_2) \geq m_1 \ln (a_1) + m_2 \ln (a_2)##.

The solution is essentially correct. Just two comments. First, you must correct the typo in the addition and the multiplication in the end of the second expression in order to be correctly written for the people that will read your solution. As a second comment, it's best to write the expansion...