Lower case a string in bash

How do I lower case a string in bash?

/bin/mv $file $(echo $file | tr '[A-Z]' '[a-z]'])

Where $file is the file name we want lower cased.

Bash endless loop

How can I execute something to run forever, like an endless loop in bash?

while [ 1 = 1 ]
   echo "Print this string forever: bash endless loop";