I feel like in this conversation you are equivocating over distinct but related concepts that happen to have the same name. For example, “numbers” in mathematics versus “numbers” in computers. They are different things - e.g. there are an infinite number of mathematical numbers but only a finite number of computer numbers - even considering bignums, there are only a finite number of bignums, since any bignum implementation only supports a finite physical address space.
In mathematics, a set of numbers is not itself number.
What about in digital computers? Well, digital computers don’t actually contain “numbers”, they contain electrical patterns which humans interpret as numbers. And it is a true that at that level of interpretation, we call those patterns “numbers”, because we see the correspondence between those patterns and mathematical numbers.
However, is it true that in a computer, a set of numbers is itself a number? Well, if I was storing a set of 8 bit numbers, I’d store them each in consecutive bytes, and I’d consider each to be a separate 8-bit number, not one big 8n-bit number. Of course, I could choose to view them as one big 8n-bit number - but conversely, any finite set of natural numbers can be viewed as a single natural number (by Gödel numbering); indeed, any finite set of computable or definable real numbers can be viewed as a single natural number (by similar constructions)-indeed, by such constructions even infinite sets of natural or real numbers can be equated to natural numbers, provided the set is computable/definable. However, “can be viewed as” is not the same thing as “is”. Furthermore, whether a sequence of n 8-bit numbers is n separate numbers or a single 8n-bit number is ultimately a subjective or conventional question rather than an objective one - the physical electrical signals are exactly the same in either case, it is just our choice as to how to interpret them