Infinity?

When you see someone taking video footage of you in a screen behind you you see an infinite number of increasingly smaller versions of you. Infinite or not?

I don't have a video, but I suspect it is similar to this where it shows a repeating image of the guitarist:
https://www.youtube.com/watch?v=pZ7wdhZ4Ti8#t=3m59s

The idea is that under the right conditions, this repeating image can continue into infinity without adjustments and that you might conceivably be staring at the infinite. In this case, I believe the guitarist would just overlap every other mirror image of himself thus nullifying an infinite number of him if the angles were correct but I'm sure you can look into a screen showing an image of the screen over and over without any overlap.

EDIT: Actually, found this video https://www.youtube.com/watch?v=c4HfvQodCM4 Is it true infinity? 

Cover up: http://www.geocities.ws/rotafan/video.html (in short: 7:23 and 18:43)