Concept
What is a number when it is viewed as a quantity?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"When you think of a number, I want you to try to erase the sequence of digits from your mind. Think of a number as what is is: a quantity. Here’s what the number seventeen really looks like: It’s just an amount. There are more circles in that picture than in some pictures, and less than in others. But in no way is it “two digits,” nor do the particular digits “1” and “7” come into play any more or less than any other digits. Let’s keep thinking about this. Consider this number, which I’ll label “A”: (A) Now let’s add another circle to it, creating a different number I’ll call “B”: (B) And finally, we’ll do it one more time to get “C”: (C) (Look carefully at those images and convince yourself that I added one circle each time.) When going from A to B, I added one circle. When going from B to C, I also added one circle. Now I ask you: was going from B to C any more “significant” than going from A to B? Did anything qualitatively different happen? The answer is obviously no. Adding a circle is adding a circle; there’s nothing more to it than that."
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