If you shoot a gun in space, the bullet would keep going

Because according to physics, the bullet in a vacuum of space would keep going at the same velocity unless acted on by another objects gravity or hitting another object. PS Wouldn't the bullet eventually stop because all existing objects exhort a pull on any other object?

If it were deep in space, then the forces of gravity would more or less balance in every direction and there would not be much of a net force to change its velocity. Of course, given enough time, its velocity would change a lot.

But you are missing something. That the bullet would stop has no meaning. Stop relative to what? The earth? The center of the galaxy? The center of another galaxy. There is no 'real' speed in the universe, just relative speed. Certainly, the Earth is no longer considered to be the center of the universe, or anything special at all. But then, no other place is either.

the bullet wouldnt fire in space because thers no oxygen to ignite it....it would move at a constant speed relative to light the fastest kind of speed there is there is actually a 'real speed' which is sunlight

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The bullet would keep going at roughly the same velocity(its acceleration would be based on the sum of all forced of gravity of other objects, which in deep space is pretty negligible). However, you are making one unwarranted assumption, and that is that the cartridge would fire at all. modern cartridges are fairly well sealed, but they are not airtight, and in order for the charge(primer/gunpowder) to combust, you need oxygen(which is not generally present in space).

Nice question. A bullet fired in space (presumably a total vacuum) will continue to to move at muzzle velocity relative to the shooter until influenced by a gravity well- and yes, if the bullet is fired directly up a local gravity well (e.g., away from our galactic center), it will slow down as it travels.

You can use the same reasoning to argue that the bullet would continue on forever, since there would be as much mass (of the universe) ahead of it as behind.