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Posted by Paul R. Martin on September 16, 2003 04:28:54 UTC

Hi Harv,

(Pardon me for stepping in here, Tim, but I just couldn't sit idly by.)

"When you say 'number' do you mean it as an appropriately drawn squiggly shape that you draw on paper (or some other background), or do you mean 'number' as in a "number of identified objects"?"

Neither. The former is called a numeral (quite different from a number) and the latter is the cardinality of a set of (real, I presume) identified objects.

The mathematical concept of number is very complex but it is nothing more than an abstract notion or idea. At its base, though, the definition of a number is a set. 'Set' in mathematics is taken as a primitive term with no definition. You may visualize some real examples, which to you signify the notion of a set. But your visualization, or the examples you visualize, have no bearing whatsoever on the abstract notion of a set. In the mathematical formalism, there is no connection at all between the notion of a set, or a number either for that matter, with anything real. The fact that there is a history of using numbers to count sheep and money does not negate that fact.

I hope that helps clear things up for you.

Warm regards,

Paul

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