Will Time Machine Backups After OS Reinstall Just Keep Going?

Hi -

I did a complete reinstall of OS X 10.6 on an old Macbook Pro (early 2010?) using the discs that came with it. (Just wanted to start fresh.) Prior to the reinstall, I'd been running Time Machine for about 6 weeks.

My question: If I now fire up Time Machine using the same back up drive, will it just keep stacking new backups on the old ones? So the backup history will show the original installation up to a certain date, and then the new installation appears?

I'm hoping that's the case, and that doing so is advisable. (I know I can just start a new backup, but I'd rather have access to the old ones.)

Once I have the backups figured out, I'll be updating to 10.7.

Any help would be much appreciated!

-Mike