Correct. Any push will send you an infinite distance, but it will take you an infinity to get there.
Interstellar travel has two problems. Distance is one of them.
The other is the fact that once you get up to speed, you have to work just as hard to slow down.
Our rockets are virtually useless. There isn't any way to carry enough reaction mass to get a proper speed.
My plan at present is to use synchrotrons to accelerate very small amounts of matter to absolutely enormous velocities as a proplusion system. We would lose little mass, and should have sufficient power to do it that way, but the thrust will be fairly low, and the acceleration will take quite a while to build up.
I have to start my trip now. I'll talk to y'all when I get a chance.