In Infinityland, people have mastered full control over Infinity. They have built registers which are capable of holding as much data as needed. There are two types of registers in infinityland which are called infinity registers:
The integer infinity register: Can hold any integer value from -inf to + inf. Costs $\$100$ .
The real infinity register: Can hold any real value from -inf to + inf with infinite precision. Costs $\$200$.
Rather expensive, are they not? Well, not actually, because the people over at Infinityland have really good compression algorithms which allow them to stash huge amounts of data in those tiny registers.
What is the lowest cost you must incur to save a list of real numbers if
The list can hold a maximum of $100$ real numbers.
The list can hold infinitely many real numbers.
In the second case, the information must be decompressible without the knowledge of the size of the list.