Well, you can't prove that God doesn't exist. The only way that you can definitively say that no God exists is if you know everything there is to know about the universe, and no one can possibly know that. For example, if you were to say that you are absolutely certain there are no nails in your house, the only way you can say that is if you've searched every bit of your house and definitively know there are no nails in your house. There's no way that we can know everything about the universe.
Likewise, it takes much more faith to believe there is no God (or no intelligent designer) and everything was created by mere chance than it does too simply accept that there must have been some intelligent designer who created the universe and is in control. I admire those people who say there is no God because they must have incredible faith to believe that. I think the problem is that people don't want to relinquish their pride and their belief that they are completely independent and in control. Which choice is more reasonable? A belief that everything occurred by mere chance, or that God created the universe. A physicist one said, "If we need an atheist to debate, I go to the philosophy department. The physics department isn't much use."
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In order to perceive the evil in our world, we must first have some innate sense of right versus wrong which must come from a supreme being. Without some supreme being defining right versus wrong, how are we to know the difference? If it is just some arbitrary human standard, then why obey it? Why are these common morals able to be seen in cultures around the world? The evil in this world is the consequence of our imperfections(sin) residing in all human beings. You know that no one here is perfect. We all have made mistakes in our lives. It's not so much God who brings evil upon the world, it is the reality that all human beings are not perfect and we all make mistakes (sin). Bin laden and his goons let their anger turn into rage and the result is 9/11. This is a clear example of the evil in the world. But also see how our nation (and perhaps the world to a small extent) have taken a small step towards uniting together (United We Stand). Almost all people in the world agree the events of 9/11 were tragic and terrorism is evil, and this has led to a small step towards making the world a better place to live in.