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    How Should I Proceed?

    Hello there! I will be studying Mathematics and Physics in University in approximately 2 months. I really enjoy Mathematics and have done some introductory Calculus. I have looked into Spivak's book "Calculus" and, although written very well, I just tent to find Calculus boring. However, when...
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    Verification of Simple Proof

    1. Homework Statement I am using Spivak's Calculus and just finished the third exercise in part 1. It was a very easy exercise but it seems that Spivak makes some assumptions. The problem is as stated: If x^{2}=y^{2}, then either x=y or x=-y. Prove it. The proof was relatively simple (by...
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    Various Proofs Regarding Divisors and Properties of Divisors

    Hello there. I have been reading G.H. Hardy's book "A Course of Pure Mathematics". It is a fantastic introduction to Analysis. I have no problems with the book so far, however, it does assume some knowledge in number theory. I just want to make sure that the following proofs for properties of...
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    Questions Regarding Nuclear Fusion

    Hello there physicists! I am here to ask a few straightforward questions regarding nuclear fusion accomplished here on Earth. Question 1: How does a magnetic field contain the heat produced by nuclear fusion in the reactor? If we look at the example of Deuterium fusing with Tritium, a high...
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    Parallelogram Paradox!

    Hi there! My question involves the area of a parallelogram. Now, I know how to prove the commonly used formula (b*h) very easily, however, there is a formula given on Wikipedia as an alternative that states....Given two sides B and C with angle (theta), B*C*sin(theta)=Area of a parallelogram...
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    Electromagnetic Radiation and Mediums

    1. Homework Statement Hello there! I have a couple of questions regarding light(EMR) and how it behaves when moving from one medium to another. From what I understand, the frequency of any light wave, when it moves from one medium to another, stays the same. As a consequence of this, the...
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    Electromagnetic Waves

    1. Homework Statement Hi there! I am currently taking physics and we are in the process of learning about electromagnetic radiation. I am a bit confused as to how exactly an electromagnetic wave is produced. I understand that a periodically oscillating charge produces and oscillating magnetic...
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    Proof of the Possibility of Division!

    Hi there! I have been reading Apostol's "Calculus: Volume 1" and have been trying to prove a few theorems using specific field axioms(note that this is not a "homework" question since I have not been assigned it, but instead, chosen to attempt it out of curiosity). Although I am not a math...
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    Prove that if ab=ac, then b=c.

    Can someone help me prove that if ab=ac and a does not equal 0, then b=c. You can only use the field axioms. Here is my attempt( I am not sure about the final result). ab=ac then, ab-ac=0 a(b-c)=0 a(0)=0 (Already proved this) since a cannot equal 0, (b-c) must equal zero and we are left...
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    Cross Product of Magnetic Field(B) and Velocity of Charged Particle(v).

    1. Homework Statement Hi there. I am currently taking physics 30(algebra physics course) and we are in the electrostatics unit. I am curious as to why, when trying to find the force acting on a charged particle moving perpendicular to a magnetic field, the force results in a direction that is...
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    Electric Potential Energy

    1. Homework Statement \ Hi there! We are currently studying forces and fields in physics and we are in the electrostatics chapter. I am having a bit of trouble fully understanding electric potential energy. The book states that electric potential energy is defined as the work required to move a...
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    What is charge really?

    1. Homework Statement The problem is that I don't understand what causes an object to become positively or negatively charged. I know that, in chemistry, ions represent charges in voltaic cells. For example, cations become reduced and their electrons travel to the anode. This creates a negative...
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    Equation of an Ellipse.

    1. Homework Statement As I was relearning some concepts in calculus, I came across a section on ellipses. What I don't understand is why a and b in the standard equation of an ellipse govern the length of the minor/major axes. Can anyone shed some light? Thank you very much! 2. Homework...
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    Euclid's Proof for Prime Numbers

    1. Homework Statement Euclid's proof Euclid offered the following proof published in his work Elements (Book IX, Proposition 20)[1] and paraphrased here. Take any finite list of prime numbers p1, p2, ..., pn. It will be shown that some additional prime numbers not in this list exist. Let P be...
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    The Range of a Function in Set Y!

    1. Homework Statement N/A 2. Homework Equations N/A 3. The Attempt at a Solution I guess I will start here. My question does not necessarily involve equations. In the Calculus book I am currently studying from, I am reviewing some pre-calculus and I came across a section that...
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