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| From my email to RS<blockquote> 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 <math>\{2n+1\}_{n=0}^\infty</math> could be properly thought of as that concept which---in appropriate contexts---subsumes the following concretes:
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| * the method that a child uses to produce the ''n''th odd number
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| * a C++ program which takes in a uint32, ''n'', and outputs 2''n''+1
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| * the following table on my screen [a screenshot of a few rows of an excel table where the entries are 2*row + 1 ]
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| * etc.
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| Or the infinite set <math>\mathbb{N}</math> 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.</blockquote>
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Latest revision as of 01:55, 21 January 2024