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Your insistence on me begging the question is really quite annoying, either learn how to identify one, or stop accusing people of it. But, we proceed: Alright then continue to provide claims that is not backed up by any evidence Even though you know there are countless arguments for...

I don't think you understand what the word heretic means In any case, if you're referring to those non-Muslims who are starving in Africa, they will be tested on judgement day to see if they would believe in the unity of God, and his Holy Messenger. It is common through all Abrahamaic faiths...

Except we believe that such people with bad circumstances in their life will be recompensed in the here-after for their suffering Also according to you and other people with disgusting naturalistic beliefs, believe that such poor children are part of natural selection, and that is simply how...

\\ \frac{5}{x^2-1} - \frac{3}{x-1} \\ \\ = \frac{5}{(x-1)(x+1)} - \frac{3}{x-1} \ \ \ $(Difference of two squares$ \ a^2-b^2 = (a-b)(a+b) \ $)$ \\ \\ = \frac{5}{(x-1)(x+1)} - \frac{3(x+1)}{(x-1)(x+1)} \\ $(Multiply second fraction by$ \ \frac{x+1}{x+1} = 1 \ $to make common denominator)$ \\ \\ =...

Re: HSC 2014 4U Marathon - Advanced Level This is a good inequality \\ $Let$\ n \geq 3 \ $be an integer, and$ \ a_2,\dots,a_n \ $be positive reals so that$ \ a_2a_3\dots a_n = 1 \\ \\ $Prove that$ \ (1+a_2)^2(1+a_3)^3(1+a_4)^4 \dots (1+a_n)^n > n^n

Re: HSC 2014 4U Marathon \\ $The quadratic equation$ \ x^2+ax+b+1 = 0 \ $has integers$ \ a,b \ $and has integer roots$ \\ \\ $Show that$ \ a^2+b^2 \ $cannot be prime$

Re: HSC 2014 4U Marathon - Advanced Level \\ $Let$ \ a,b,c,d \ $be positive reals that sum up to 1$ \\ \\ $Show that$ \ \ \frac{a^2}{a+b} + \frac{b^2}{b+c} + \frac{c^2}{c+d} + \frac{d^2}{d+a} \geq \frac{1}{2}

Re: HSC 2014 4U Marathon - Advanced Level I haven't gotten around to grounding myself well yet, I still don['t know what eigenvectors/values are

Re: HSC 2014 4U Marathon - Advanced Level Using Prime numbers gives all the board: Black blocks are blocks where the knight has not ended Red blocks are blocks where the knight has ended. The number of iterations shows how many times it has been done, and shows the various positions it has...

I open a fortune cookie it says "The Earth is round" Do I conclude, "Oh, the statement in this fortune cookie must be false because this information comes from a fortune cookie"? Of course not. Your point about the origins of religion completely sidesteps the issue at hand, it explains...

Re: HSC 2014 4U Marathon - Advanced Level I think we can still make the same argument as before, but instead of alternating between 2, we alternate between 4 instead. Since 4000/4 is an integer, we can still arrive on everything using a '4-cycle' What would be interesting is that if instead...

I was hoping for a meaningful response: My bad there, I was operating under a misconception Completely understandable, but then you would have to concede that it is false that there is no evidence for the existence of God. Not at all, the creation of the universe is itself an active act...

Re: HSC 2014 4U Marathon - Advanced Level Also in case anyone is interested, if we take the additional condition that one cannot go back on the move the next turn, i.e. (0,0) -> (1,2) -> (0,0) is invalid We still get the whole half of the board (according to my generated diagrams)

Re: HSC 2014 4U Marathon - Advanced Level Yes that is true, my bad

Re: HSC 2014 4U Marathon - Advanced Level I have made a program to simulate this in Java. It seems we can get squares of different colour to A1, its just that my 'strategy' will guarantee every square same colour as A1, but there may be more solutions using different strategies If you have...

Please point to the argument(s) you contend with, and illustrate which premise is false, giving evidences Otherwise your post has no use

Re: HSC 2014 4U Marathon - Advanced Level Can the Knight go to the position it was the previous move? i.e. A1 to B3 to A1 again If this is so, I am pretty sure it can go on all squares of the board, because at some point in the moving, say I want my end position to be (x,y). I can just go to...

> no evidence for the existence of God no no

Proof Number 6: The Modal Ontological Argument 1. It is possible God exists 2. If it is possible God exists, then God exists in some possible worlds 3. If God exists in some possible worlds, then God exists in all possible worlds 4. If God exists in all Possible worlds, then God...

Proof Number 5: The Argument from Contingency (The Leibnizian Cosmological Argument) 1. Anything that exists has an explanation of its existence, either in the necessity of its own nature, or in an external explanation. 2. If the Universe has an explanation for its existence, and that...