[linux] Explaining the 'find -mtime' command

I'm trying to remove all the dateed logs except the most recent. Before I execute a script to remove the files, I want to of course test my commands to make sure I'm bringing up accurate results.

When executing these commands the date is:

Sep  1 00:53:44 AST 2014

Directory Listing:

Aug 27 23:59 testfile.2014-08-27.log
Aug 28 23:59 testfile.2014-08-28.log
Aug 29 23:59 testfile.2014-08-29.log
Aug 30 23:59 testfile.2014-08-30.log
Aug 31 23:59 testfile.2014-08-31.log
Sep  1 00:29 testfile.log

I thought -mtime +1 was supposed to list all files over a day old. Why isn't the 8-30.log one listed?

find . -type f -mtime +1 -name "testfile*log"
./testfile.2014-08-27.log
./testfile.2014-08-28.log
./testfile.2014-08-29.log

This is the desired effect, but it was just trial and error. What is this 0 saying?

find . -type f -mtime +0 -name "testfile*log"
./testfile.2014-08-30.log
./testfile.2014-08-27.log
./testfile.2014-08-28.log
./testfile.2014-08-29.log

+1 means 2 days ago. It's rounded.

To find all files modified in the last 24 hours use the one below. The -1 here means changed 1 day or less ago.

find . -mtime -1 -ls