Why the most famous time travel paradox is no paradox

Strictly speaking it is impossible to not travel in time. :P (except in some crazy theories where nobody knows weather they are true - like the big bang theory :mischief:)
But I don't think this question belongs into this thread.
For instance, I have no problem with assuming that to travel back in time is impossible. Actually, I am rather convinced of it. But if we assume it was possible - we can still discuss the implications. And for why that is fascinating? In my case, I don't believe that a ridiculous premise sanctions ridiculous conclusions. Okay that is admittedly rather pompous. The truth? I felt I had something important to share on this topic and it made me feel good to do so and argue it. All while convinced that one can not travel back in time.
 
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