In the following we use the assumption that the number of different atoms on ear

Question

In the following we use the assumption that the number of different atoms on earth is finite. Furthermore, we say that any possible composition of a finitely many atoms is called a molecule. Note that a molecule can have several occurrences of the same atom. We say two molecules are equivalent if both the sets atoms and the number of occurrences of each of those atoms of the respective molecules are equal. Finally, the molecule universe is defined as the set of all possible molecules.

a) Is the molecule universe countable? Provide a proof that shows correctness of your answer.

A molecule group is a finite or infinitely large collection of different molecules from the molecule universe.

b) Is the set of all molecule groups countable? Provide a proof that shows correctness of your answer.

Explanation / Answer

a) Is the molecule universe countable? Provide a proof that shows correctness of your answer.

Yes, the molecule in the universe is countable because:-

b) Is the set of all molecule groups countable? Provide a proof that shows correctness of your answer.

Yes, even the molecule groups are countable:-

Please let me know in case of any clarifications required. Thanks!

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