jimtony, thanks for you help. I think I've figured it out.
I had a suspicion that if it was not a path error, then it might be a linking error, to some packages that weren't installed to allow the file to run.
I am running 64bit ubuntu, but I had read somewhere earlier that I would need some 32bit libraries to run the Android SDK. After some hunting I found out which of those libraries I needed, and that I did not have them already installed.
I just now did:
sudo apt-get install ia32-libs
and the packages were downloaded and installed. Now typing
at the prompt gives me a help menu for the Android Debug Bridge, which is what I was expecting before. So, great!
Thanks for your help!