shah_nosrat

I'm not discouraging branding your products. Of course, no one would want their new shoes or any product they buy to be destroyed by shipping, I was suggesting of finding new ways to package the products we buy by making the packaging more compact and less excessive. Yes, I agree recycling is one of the solutions (I was reading up on Japan's recycling policies, and I think it should be a model to adopt by the rest of the world), but there are also biodegradable packaging solutions as well. I appreciate your feedback and opinion Interesting video, nice to see some initiative being taken. Thank you for your feedback!

Hi, One wouldn't really know why, because we don't have a UFO to reverse engineer and examine it, and if we do it hasn't been revealed to the general public. My best guess would be that our 'Flying' machines let it be aeroplanes have been engineering to fly in our atmosphere, like for example any Airfoil (wing) of an aeroplane is designed to produce lift relative to the wind, as for rockets I wouldn't know of. Now the UFO's one would assume is capable of space travel, although they are also capable of flying in our atmosphere, one should question its mode of propulsion that it uses. Although there might be a reason for it's shape and design, but we yet don't know and it's mainly speculation.

Hi, I was thinking about this for quite a while now. Practically everything we buy is packaged in some form or another, like for example: food, electronics, shoes, accessories, games......etc. Is there a way to be minimalist about how we go about packaging our 'stuff' and try to reduce waste. Or employ biodegradable materials in our packaging?

If you want to get a good understanding of the thinking processes involved in Mathematics, and going about proving statements, try reading books on 'Transition to Advanced Mathematics'. There are many books out there. I'm using the following book: Mathematical Thinking and Writing - A Transition to Advanced Mathematics by Randall B. Maddox. It gives good guidance. Hope this helps

Thank you!

Here the question I need to prove followed by my attempt at the solution; [math] \bigcup_{\beta \in \mathcal{B}} A_{\beta} \subseteq \bigcup_{\alpha \in \mathcal{A}} A_{\alpha} [/math] and suppose [math] \mathcal{B} \subseteq \mathcal{A} [/math] My attempt at the solution, as follows: Let [math] x \in \bigcup_{\beta \in \mathcal{B}} A_{\beta} [/math] such that for some [math] (\beta \in \mathcal{B}) [/math] we have [math] x \in A_{\beta} [/math]. Now, Pick [math] \beta \in \mathcal{B} [/math] , since [math] \mathcal{B} \subseteq \mathcal{A} [/math] we have [math] \beta \in \mathcal{A} [/math]. Hence we have [math] x \in A_{\alpha} [/math] for some [math] \alpha [/math]. Which follows: [math] x \in \bigcup_{\alpha \in \mathcal{A}} A_{\alpha} [/math] Is the above proof correct?

What you mentioned above concerning [math] lim_{n \to \infty} (1 + \frac{1}{n})^{n} = e[/math] is the definition of [math] e[/math] . But if you'd like to know how, you should consider the sequence [math](1 + \frac{1}{n})^{n}[/math] and see if it converges, and which it does. Now, as to why [math] e[/math] is so special is because it is built in the definition of compounding. [math]A = P(1 + \frac{j_{m}}{m})^{tm}[/math] where [math] j_{m}[/math] is nominal annual rate, let t = 1. As [math] lim_{m \to \infty} (1 + \frac{j_{m}}{m})^{m} = e^{j_{m}}[/math]. [math] A = Pe^{rt}[/math] where [math] r[/math] is the continuous compounding that occurs. Which can be related [math]e^r = (1 + \frac{j_{m}}{m})^{m} [/math]. Hope this helps.

Calculus has many applications! But if I understand your question properly, you'd like to know what Calculus is? If you take up a course in Real Analysis, this sets the stage for the rigorous study of Calculus.

Hi, You can use the product and chain rule together. Remember the product rule says to differentiate [math]3x[/math] and keep [math](x^2 + 4)^-1[/math] and continue the procedure (which can be found in any Calculus Textbook) and also remembering the chain rule when differentiating [math](x^2 + 4)^-1[/math] Now, [math]=-3x(2x(x^2+4)^-2[/math] this is one of the terms but you're missing one more term to get the answer NB: Using the quotient rule is more direct! Hope this helps!

Thanks for the guidance! Really appreciate it!

Isn't this closeness to God! This works with faith. Mystics by definition is: Someone who believes in realities beyond human comprehension. Now a mystical experience is purely subjective. That was merely an example I used, not to be taken literally. That is true that is being submissive to the will of God. References: 1 Philosophy: Who Needs It by Ayn Rand

I'll go about doing this, here is my attempt at the solution: Let a; b > 0 then a + b > 0. Now, 2 > 0 and a > 0, then 2a > 0. write 2a = a + a, hence 2a = a + a > 0, since a < b we find that a + a < a + b. Also, 2b = b + b > 0, where a < b. we have a + b < b + b. And so 2a < a + b < 2b. That was for the case a, b > 0. Now if you want to consider for any real number, I will use the following result (Which I have proven earlier.) Result: If a < b, then a + c < b + c. to show that 2a < a + b, using the above result, set c = a. And, similarly to show that a + b < b + b = 2b, using the above result, set c = b. Is this correct? Also what does the author mean by: Should I say it's the multiplicative of 2-1 Once again your help is appreciated . Kind Regards.

I didn't mean to say that where our destination is, I just wanted to point out that heaven or hell is not a physical place. As to the point you made about the Christian mystics; that's all they are mystics, much like Sufism. I never denied the existence of heaven or hell, I merely pointed out that it is not a geographical place where we can transport ourselves there physically. Well my finite senses is all I have to go on to make sense of my world and reality. Once again this was my reiteration of the point I made above, Heaven or Hell is not a Physical reality. Well this is what we humans 'desire' and is our interpretation of what Heaven is.

Hi, It's a very interesting question you have . First of all one has to make the observation that this physical reality is the only reality that is physical. What I mean is that if we die there is no physical place known as hell or heaven that we go to. If there were, wouldn't we be able to find it! Secondly the concept of heaven or hell as mentioned in many holy books is simply a state of reality: for example 2 people in the same room, can be in two different states, one can be in a joyous, peaceful and blissful state, whereas the other being in his own 'Hell' state. Which in itself can be an informal proof, as to you don't have to be in different places to experience different states. Now to expand this would be to understand that: "Physical pain is left behind with the death of the physical body. The hell-fire that the soul can feel is the fire of separation, the dreadful pain of being kept away from the nearness and beauty of God. This pain is real hell and worse. So Heaven and Hell are not a matter of geography. Closeness to God is Heaven, remoteness from Him is Hell1." This simply means that as human beings, we are not creatures of the physical form, although we inhabit a physical form (This may seem contradictory). We are simply a state of consciousness and our experiences are afforded through the interplay of the mind - body - spirit. Now one may ask to define what it means by the mind - body - spirit but that's a different discussion. If you require proof of the existence of God an interesting read would be the book called: Love, Power, and Justice: Dynamics of Authentic Morality by William S. Hatcher, who is a Mathematician, Philosopher, and Educator. There a section in the Appendix that is: Sketch of Formalized Version of the Proof of the Existence of God. Hope This helps. References 1 The Baha'i Faith: A Portrait by Sarah Zarqani - Rene.

I've come across this fantastic book recommended by a friend, it's written by Professor William S. Hatcher who is a Mathematician, Philosopher (Platonic philosopher), and Educator. The Book is called: Love, Power, and Justice: The Dynamics of Authentic Morality, which explores issues of authentic morality. The author does it in a very interesting manner by introducing definitions and axioms, and going on to producing proofs based on the assumptions made. It also has in the appendix II: "Sketch of Formalized Version of the Proof of the Existence of God." Very interesting read.

HI, I would suggest that you build your own case, as it's much easier to compartmentalize the case according to your needs, and it's much more economic. Also I would discourage incorporating your Xbox in the same case as your system units components, simply because your Xbox has different cooling needs, but if you decide to do so make sure that you place your Xbox in a separate closed off compartment above your system units components to reduce any problems with your gaming unit suffering from heat. As for cooling, using a water cooling system is quite pricey and installation a hassle. My suggestion for your cooling needs which will rid your PC of producing excess heat and noise, would be to do 2 things, as follows: Get an effective heatsink Get an effective fan Now, the following are some suggestions and ideas how to go about it: Get the Arctic HC01 - TC hard drive cooler and silencer: $25 - 35 : It kills the noise your hard drive makes and keeps it cool. Tuniq Tower 120 Extreme CPU Cooler: $65-75 Sunbeamtech Rheosmart 6 Fan: $40-50. or the Aerocool FP - 01: $50-60: The above two are fan regulators and allows you to adjust the speed at which your many fans run at, and can reduce noise. Hopefully this helps. Kind Regards.

Some of the Scientists (not necessarily the above mentioned ) were from an aristocratic family, so they may have been in a better position to pursue academic endeavors, however, regardless of what money the above mentioned Philosophers and Scientists made, I think they were more interested in making contributions to human knowledge and the advancement of that knowledge. Kind Regards.

Hi, Thank you very much for your quick reply. I see your point, but I took the question directly out of the textbook. Maybe the author forgot to put in the parentheses. How would one go about proving the above statement, as you stated. I will start working on it as well, before looking at your reply. Much appreciated .

Hi Guys, I'm Shah_Nosrat, Hoping to LEARN and exchange ideas on SFN! Regards.

Hi Guys, I've been stuck with the proof of this particular statement, specifically the comments at the end of the statement. As follows: Prove that If a < b are real numbers then a < a + b/2 < b. (How do you know that 2 > 0#? What exactly is 2?) My attempt, as follows: since a < b, then 0 < b - a (by definition.) *assuming that we know what b/2 is, and that b/2 < 0 such that -(b/2) > 0 then, we know that: b - a - b/2 = b - (a + b/2) > 0 ----> b > a + b/2. NB:[-a - b/2 = -(a + b/2) can be justified] the a< a + b/2 ---> don't know how to go about proving this part! *Can this assumption be justified. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #I know that 1 > 0 (I've proven this in an exercise. Using the Trichotomy Law and that for any a in R, we have a2 > 0.) Using that fact, we have 1 + 1 = 2 > 0. is this correct ? %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Your help is most appreciated .