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The intuition behind them is the reason yes, these arguments are merely attempts to change intuition to formal argumentation. i.e. clear intuitive design in creation, why do we exist, clear meaning in life etc etc. No, God is not an uncaused beginning. I don't know where you got this concept...

Proof Number 4: The Kalaam Cosmological Argument 1. Whatever begins to exist has a cause. 2. The universe began to exist. 3. Therefore, the universe has a cause. Defense of Premise 1: This again is obvious, for a more comprehensive explanation, please see Proof Number 1.2 We know...

Proof Number 3: The Teleological (Fine Tuning) Argument 1. The fine-tuning of the universe is due to either physical necessity, chance, or design. 2. It is not due to physical necessity or chance. 3. Therefore, it is due to design. Defense of Premise 1: This really comes into 2 parts...

Proof Number 2: The Moral Argument 1. If God does not exist, objective moral values and duties do not exist. 2. Objective moral values and duties do exist. 3. Therefore, God exists. NOTE: This is not the professional defense of the argument, I'm using what I have thought of...

Proof Number 1: The Occasionalist Argument 1. [I lift my hand in real life, point to it and say,] This particular movement of my hand is something which began to exist. 2. Whatever begins to exist must have a cause. 3. Therefore, this particular movement of my hand must have a cause...

So will you be able to argue against the 17 variations of the cosmological argument, the teleological argument and its forms, the moral argument, and various ontological arguments? Why are you so certain in claiming the lack of evidence for the existence of God? As far as I'm concerned the...

Re: HSC 2014 4U Marathon \\ $Let$ \ a,b \ $is real, and such that$ \ \ \frac{a+b}{a-b} + \frac{a-b}{a+b} = 6 \ $and$ \ |a| \neq |b| \\ \\ $Find the value of$ \\ \\ \frac{a^3+b^3}{a^3-b^3} + \frac{a^3-b^3}{a^3+b^3}

Re: HSC 2014 4U Marathon - Advanced Level Yep this was my method, well done. Yes this was also my solution, nice.

Re: MX2 Integration Marathon \\ \ \int_0^{n\pi} |x\sin x| \ dx \ $where$ \ n \ $is an integer$

Re: HSC 2014 4U Marathon - Advanced Level \\ $Find, with proof (without using L'Hopitals Rule)$ \\ \\ \lim_{x \to 0} \frac{\ln(\tan \left(x + \frac{\pi}{4} \right))}{\tan x}

Re: HSC 2014 4U Marathon - Advanced Level \\ $A polynomial$ \ P \ $is irreducible over the integers if there exists no$ \ R, S \ $integer polynomials so that$ \ P = R \cdot S \\ \\ $Consider the polynomial$ \\ \\ f(x) = (x-a_1)(x-a_2) \dots (x-a_n) - 1 \\ \\ $Where$ \ n \ $is odd and$ \...

Re: HSC 2014 4U Marathon - Advanced Level \\ $If a polynomial$ \ P \ $is reducible, then$ \ P = R \cdot S \ $for integer polynomials$ \ R,S \\ $If$ \ P \ $is prime, then$ \ R=1, S=P \ $or$ \ R=P , S=1 \\ \\ $Then if there are infinite inputs to get an infinite amount of primes for output...

Re: HSC 2014 4U Marathon - Advanced Level My bad my wording is wrong \\ $Prove that if an integer polynomial$ \ P \ $is reducible over the integers, then$ \ P \ $cannot output an infinite amount of primes, given integral input$

Re: HSC 2014 4U Marathon - Advanced Level \\ $Prove that if an integer polynomial is reducible over the integers, then the factor polynomials can not out put an infinite amount of primes (when given an integer input)$ EDIT: disregard

Re: HSC 2014 4U Marathon - Advanced Level \\ $Given a regular pyramid with a triangular base set in a two-dimensional plane, select any edge of the three sides of the face touching the plane and use the edge as an axis to turn over the pyramid. Find the probability that, after repeating this...

Re: HSC 2014 4U Marathon - Advanced Level \\ $A triangle$ \ ABC \ $has medians$ \ m_A, m_B, m_C \ $with sides$ \ a,b,c \\ \\ $Show that$ \ \frac{3}{4}(a^2+b^2+c^2) = m_A^2 + m_B^2 + m_C^2

Re: MX2 Integration Marathon That looks like a different form to what I had but correct, well done, all I did was: \frac{\sec x}{3 - \cos^2 x} = \frac{1}{\cos x (3-\cos^2x)} = \frac{1}{3} \left(\frac{1}{\cos x} + \frac{\cos x}{2 + \sin^2 x} \right) Which is easily integratable

Re: MX2 Integration Marathon \\ \int_0^{\pi /4} \frac{\sec x}{2 + \sin^2 x} \ dx

Re: HSC 2014 4U Marathon Yea I guess that would work, I was expecting something to do with cis() but its the same thing

Re: HSC 2014 4U Marathon - Advanced Level Yep I got that as well. What I did: u_n = \left(\frac{(2n)!}{n^nn!} \right)^{1/n} 2u_n^n \frac{2n+1}{n+1} \frac{1}{(1+1/n)^n} = u_{n+1}^{n+1} \lim_{n \to \infty} u_n = L L = 4e^{-1}