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Re: HSC 2014 4U Marathon \\ $Prove that$ \ \ 1 - \frac{2}{\pi} x \leq \cos x \leq 1 - \frac{x^2}{\pi} , \ $for$ \ 0 \leq x \leq \frac{\pi}{2}

Re: The Nonsense Thread Why is the first premise wrong? Clearly t=0 and t=15 or whatever have no discrimination in between, so why should there be an uncaused event happen at t=0 but not t=15? Anyway I think I'm getting what you are saying though You are saying that causality in essence is...

Re: The Nonsense Thread Yes that looks right to me, the reason why we even say that our souls are potentially eternal, is because according to scripture, we will have eternal afterlives, meaning our existence will be eternally sustained by God meaning our souls are potentially eternal. Hope...

Re: The Nonsense Thread Hang on so what is your definition of the universe? If the universe is all that there is, then God would be inside the universe, but that is fine because in our argument, we simply change the word 'universe' to 'physical universe'. Then we can simply apply the notion...

Re: The Nonsense Thread All attributes of God are indeed unique, the ones that we can arrive at through pure reason though, include His pre-eternality, and to suggest that there are other beings that can have this attribute at least in my view is akin to polytheism. To have our souls be...

Re: The Nonsense Thread But God is timeless as He is not bound by time, meaning God existed independent of time t, and created the universe, therefore creating the universe. The issue you quoted is an issue with what is seen as the relational theory of time.

Re: The Nonsense Thread Yep, God is seen as pre-eternal by clear consensus. I could also ask the question of what purpose would a spiritual ascension do over a bodily resurrection which would surely be more invigorating and 'real'. The point being with the soul and why it being eternal is a...

Re: The Nonsense Thread He definitely experienced a lot of criticism from what you'd probably call the 'clergy', though at his time the Mu'tazila sect which is a sort of moderate version of Ibn Sina and Al-Farabi and would be more sympathetic of them, they were essentially rising in...

Re: HSC 2014 4U Marathon - Advanced Level An attempt at a more formal solution: \\ f \ $is differentiable on$ \ (a,b) \ $using this fact, prove that$ \ f' \ $is continuous on$ \ (a,b) \\ \\ $For$ \ f' \ $to be continuous on$ \ (a,b) \ $then$ \\ \\ \lim_{x \to c} f'(x) = f'( c) \ $for all$ \...

Re: HSC 2014 4U Marathon - Advanced Level \\ $Find the minimum value of the function$ \ f(x) = \int_0^{\frac{\pi}{4}} |\tan t - x| \ dt

Re: HSC 2014 4U Marathon - Advanced Level \\ $Since$ \ f' \ $is non-constant, there must be some real$ \ c \in (a,b) \ $so that$ \ f'(c) \geq f'(x) \ $or$ \ f'(c) \leq f'(x) \ $for$ \ x \in (a,b) \\ \\ $By comparing areas$ \\ \Rightarrow \ \left|\int_a^b f'(c) \ dx\right| \geq \left| \int_a^b...

If you knew where that would lead you philosophically I am sure you would retract that statement pretty quickly If everything is just chemical reactions in our brain, then there is no true libertarian free will, meaning no one is accountable for morality. i.e. a serial killer is just acting on...

I have not used the Muslim belief as a form of proof, rather I have not even given any proof in my statement, I was simply giving a brief outline to seanieg of how I would go about showing that Islam is the most coherent religion If I wanted to show that God cannot come down in the form of a...

It only takes a bit of logically progressive arguments to arrive at One, All-Powerful, All-Knowledgeable Creator, using what we already know from the Fine-Tuning argument and the Cosmological Argument. Then relying on biological teleology we may deny Deism and affirm Theism, i.e. a Creator who...

Well any intelligent atheist doesn't believe that "it just happened by chance", they will do anything they can do, to distance themselves from the charlatan Dawkins, they have proposed various metaphysical theories such as the level 2 Multiverse theory in order to explain the cosmological...

Can you read? Ah but I've proven that the specified probability is different to spilling marbles on a floor, and in fact does mean a lot, showing that if we only a small finite number of universes exist, the specified probability is so vanishingly small that the conclusion must be design. On...

Re: HSC 2014 4U Marathon - Advanced Level \\ $The numbers$ \ -1 \leq x_1, x_2, \dots, x_{n-1}, x_n \leq 1 \ \ $satisfy$ \ \ \sum_{i=1}^n x_i^3 = 0 \\ \\ $Prove that$ \ \ \sum_{i=1}^n x_i \leq \frac{n}{3}

Re: HSC 2014 4U Marathon - Advanced Level \\ $A)$ \ \lim_{x \to 1} \frac{f(x) - x^2 f(1)}{\sin (x-1)} \\ h=x-1 \\ \Rightarrow \ \lim_{h \to 0} \frac{f(1+h) - (1+h)^2}{\sin h} = \lim_{h \to 0} \frac{\frac{f(1+h) - 1}{h} - h +2}{\frac{\sin h}{h}} \\ \\ \frac{\lim_{h \to 0} \frac{f(1+h) -...

Re: HSC 2014 4U Marathon - Advanced Level This is a good question \\ $Let$ \ f(x) \ $be a function on$ \ a \leq x \leq b \ $and differentiable on$ \ a < x < b, \ $and also $ \ f' \ $is non-constant$ \\ \\ $Prove that there exists some$ \ a \leq c \leq b \ $such that$ \\ \\ |f'(c)| >...

Umm what? It is undisputed that the constants required for the existence of a universe sustainable for life are on a knife's edge of improbability The dispute comes about whether the constants had come about through pure chance or by design, and its the Fine Tuning argument which proposes that...