Ceci n'est pas une pipe.

Is that Maigret?

Oui.

But there are more raindrops than clouds and there is an infinite number of shapes and sizes of clouds?

Yes, and yes. And, oddly, there are (theoretically) more cloud shapes than there are real numbers. (the cardinality of the (which means, roughly, "number of") functions of real numbers is greater than the cardinality of the real numbers themselves.
A function is a set of real number pairs (+). Each such set is a subset of the real numbers. So the set of possible functions is essentially the set of subsets of real numbers. This has greater cardinality. ("There are more of them.") Which is
what you realize below when you say:

I do now understand the point that where you can map an infinite number of sub objects to each integer it implies some substantial difference in kind (scale? extent? Infinity? Whatever).

It has a greater cardinality. But I'm talking about the case where the "map" is done by considering the set of subsets. Not every infinite map will give a greater cardinality. There are an infinite number of fractions with any given integer in the
numerator, but the number of fractions ("rational numbers") has the same cardinality as the integers ("there are just as many of them, no more, no less")

Will it help with my dabbling in aerodynamics I wonder?

No. But it will help pass the time if you get bored with it.

Jose

(+) ok, they are ordered pairs such that the first element can only occur once in the set. For example:
{(2,4) , (3,5) , (4,5) } (the set containing the three ordered pairs (2,3), (3,5), and (4,5)) is a function, but
{(2,4) , (2,5) , (4,5) } (the set containing the three ordered pairs (2,3), (2,5), and (4,5)) is not. (It's a relation though)
Essentially, for each and every first element, there can only be one second element associated with it. Therefore, the cardinality of the function is equal to the cardinality of the first elements of the function. (there are exactly as many ordered
pairs in the function as there are distinct first elements in the function.)

--
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