To this point, cron's default behavior is to email all output to the user whose crontab invoked the process. Often times, the crontab output is redirected somewhere else , /dev/null being a popular choice, or other useful log file.

I tend to have my cron processes email success emails to one address, and failure to another address.

Good sysadmin's hook their processes into their favorite monitoring tools, TMTOWTDI.

--Fred