> You could also say for (0..$a_big_number) { ... }, but that is no way to save memory.

Actually, it is. For some time now that style of foreach loop has been optimized. It doesn't create a list of $a_big_number+1 elements; it efficiently iterates one at a time through the set, much as the equivalent C-style for loop would.

You can prove this to yourself by using a really big number and watching the memory of the program as it runs (say, through top):

foreach (0..100_000_000) { $i++ }
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Compare this with the memory usage of something like the following. Notice I had to drop the number from 100 million to just one million; 100 million caused perl to die with an out of memory error.

@array = (0..1_000_000);
foreach (@array) { $i++ }
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This optimization was added to perl 5.005; perldoc perl5005delta mentions it, search for 1000000.