[user104658]

Ahh the grandfather paradox. "But if you never existed then you didn't kill him, so he lived, so you do exist, so you could kill him."

There are really only three options here:

#1 Multiverse theory. This is essentially how "Terminator time travel" works according to the most recent, most crappy film and many other Sci fi stories. Basically, each decision creates a new timeline but doesn't erase the old one. So, you in timeline A go back and kill your grandfather in timeline A, creating timeline B where everything is different. However, timeline A still exists in parallel and so you (being from timeline A) still exist. This is the least problematic time travel variation.

Option #2 The future is erased as soon as you travel back. Nothing past the point of arrival ever happened and you and anything you brought back are now an "anomaly". Your actions now create the new future. Killing your grandfather doesn't do anything, because that future is gone but you are still "from there". Sort of like a copy and paste, I suppose.

Option #3 Time travel is impossible because, if it were possible, it would be happening constantly (because infinity) meaning that there is no such thing as reality at all. Reality would be in a blender.

Option #4 the grandfather paradox is alive and well but no one has discovered time travel YET. As soon as someone does, they go back in time, any tiny change they make disrupts the future (doesn't need to be as severe as killing an ancestor - the butterfly effect suggests that a no number of tiny alterations might stop you from existing, stop time travel being invented, change future motivations etc.) and then the paradox activates and the universe implodes from that point onwards. Luckily, the first person to discover it didn't travel back as far as 2015 in human years.