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Challenge #1: Produce a Surah equal in Beauty, Literary Value, Eloquence (etc.) like the Holy Qur'an (all)
The Koran is easily the most important work to come out of the Arabic-speaking world. However, its significance is based on its involvement within that culture. It does not have as significant meaning or beauty to a non-muslim or non-arab speaker as a plethora of other literary works. For myself, The Great Gatsby and the Declaration of Independence are far more important works in my culture with amazing uses of the English language.
You're basically asking us to provide a greater piece of music than Beethoven's 12th. symphony. It's pretty subjective and based on the culture of the person.
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Challenge #2: Produce a fly (all)
I'll address this one below. But for now, I'd say it's not an easy process, but cloning flies is quite possible.
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Challenge #3: Find a contradiction within the Arabic context of the Qur'an (all)
One of the issues I have with Islam and the Koran is the rejection of the Old and New testament (due to their supposed corruption from being written by men, not God), yet the acceptance of Christ being able to preform miracles. Or that previous prohphets (such as Abraham and Moses) even existed. The Koran and Islam pick and choose from what texts are still applicable from Judaism and Christianity.
It is quite silly to accept there are blatant contradictions in the bible, yet accept the over-the-top miracles and events depicted.
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Challenge #4: How did something come out of nothing? (for atheists)
Like #2, this argument can easily be made from a Christian or Jew and does nothing to prove Islam is true. That being said, abiogenesis is completely compatible with Islam, as is evolution. However, neither one claims to have something come out of nothing. The simple bottom line is that matter cannot be created, nor can matter be destroyed. It can move around, but that's it, which is exactly what evolution and abiogenesis are about.
As far as the Big Bang goes, scientists are operating under the hypothesis there was something before the big bang. All the big bang explains is the universe as we currently know it from a single point in time. It doesn't go into explaining what came before. The short answer is that we just don't know yet, but we're working on it.
My counter-claim for you then becomes: How did God come to exist? Did he come from nothing?
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Challenge #5: Answer the difficulty of Mark 16:15-18 (for Christians)
Challenge #6: Prove that Muhammad/Islam is the Anti-Christ when your own Bible confirms the two!!!
Challenge #7: Prove that Jesus is God when he himself testified in John 17:3 that the "Father" is the *only True God*!
Challenge #8: Prove that Jesus was not refuting the crucifixion when he gave two CLEAR prophecies against it!!!
Challenge #9: Prove that the Bible is the word of God when it (the Bible) clearly says no!!!
Challenge #10: Prove that John 1:21 has nothing to do with Deuteronomy 18:18...
These are all nitpicking texts within the Bible that goes back to my answer in #3. These are also arguments against Christianity and Judaism, but not arguments for Islam. Any non-christian or non-Jew could make these arguments.
So far, the only thing you've said in the defense of Islam is that the Koran is a really well-written text with a lot of wisdom. Everything is just miscellaneous ramblings about how other people's beliefs are wrong. But just because someone things 1 + 1 = 3 and you think the answer is 4 makes neither one of you correct.
As you like to say: CASE CLOSED!