I forgot whether the MEPIS 7 version that I installed is 32-bit or 64, and I must admit that I don't know the difference. (All I know is that my new computer here is able to run 64-bit OSes, whatever those are.) What can I check to find out?

-if you see 'amd64' or 'x86_64', then you are probably 64-bit.
-Also, if you see 'i386', 'i686', etc, you're probably running 32-bit.
-Yet another way is to look for a 'lib64' directory in the root file system. It will be there only if your are running 64-bit.

Another useful command to find out:

More than "probably". For 64-bit Mepis the output will include 'x86_64' and for 32-bit Mepis it won't.

Also more than "probably". uname -a in 64-bit Mepis will not say 'i386' nor 'i686'. I'm pretty sure in 32-bit it will say 'i686'.

That works too.

Lots of other threads here discuss the relative merits of using 32-bit vs. 64-bit, usually without a clear conclusion.

I'm very happy with 64-bit Mepis. I haven't run into any compatibility issues, and I can't think of any reason to choose 32-bit instead of 64-bit for a reasonably configured, fairly new computer, used for any ordinary purpose.

But if you already installed 32-bit Mepis, it probably also isn't worth the trouble to switch. For an ordinary computer used for ordinary purposes, you probably wouldn't notice any difference.

Okay. That answers my questions. uname -r says "i686," so I must have 32-bit. I'll keep it.