Answer:
To understand the answer to this question, we first need to clarify what it means for a language to be "over" an alphabet. In the context of formal language theory, an alphabet is a finite set of symbols, and a language is a set of strings made up of those symbols. So, when we say a language is "over" an alphabet, we mean that the strings in the language are composed of symbols from that alphabet.

Countable vs. Uncountable Sets:
In mathematics, there are two types of sets: countable sets and uncountable sets.

- A countable set is one that can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). In other words, the elements of a countable set can be listed in a sequence.

- An uncountable set, on the other hand, is one that cannot be put into a one-to-one correspondence with the natural numbers. Its elements cannot be listed in a sequence.

Countably Infinite Languages:
A language is countably infinite if it can be put into a one-to-one correspondence with the natural numbers. In other words, the strings in the language can be listed in a sequence, where each string corresponds to a natural number.

If the alphabet is finite, then the set of all possible strings over that alphabet is countably infinite. This is because we can list all the strings of length 1, then all the strings of length 2, and so on. Each string can be assigned a unique natural number, and thus the set of all strings is countably infinite.

Uncountable Infinite Languages:
However, if the alphabet is infinite, then the set of all possible strings over that alphabet becomes uncountably infinite. This is because there are infinitely many symbols to choose from for each position in a string, and each position can be assigned a symbol independently.

For example, if the alphabet is the set of real numbers R, then the set of all possible strings over R is uncountably infinite. This is because for each position in a string, we can choose any real number, and there are uncountably many real numbers.

Conclusion:
In the given question, the alphabet is R, which represents the set of real numbers. Since the set of all possible strings over R is uncountably infinite, the correct answer is option 'D' - uncountable infinite.