Sequences

From my email to RS

 I have noticed that there are many specific "infinite sets" that I think are---or rather, are philosophically sloppy stand-ins for---valid concepts. For example, the infinite (ordered) set $\{2n+1\}_{n=0}^{\infty }$ could be properly thought of as that concept which---in appropriate contexts---subsumes the following concretes:

• the method that a child uses to produce the nth odd number
• a C++ program which takes in a uint32, n, and outputs 2n+1
• the following table on my screen [a screenshot of a few rows of an excel table where the entries are 2*row + 1 ]
• etc.

Or the infinite set $\mathbb {N}$ is just a stand-in for the concept of natural numbers, which subsumes the concepts 1, 2, 3, etc, which in turn subsume concretes like 1 apple, 2 oranges, 3 bananas, etc.