You're going to find a lot of math awfully hard to do if you can't think about any uncountably large collections.
The phrase "uncountably large collections" isn't uncountably large. Your brain is a finite object or finite size and there is a limit to the complexity of the things it can think about. The concept of "uncountably large" is not sich a complex thing.
I don't really do maths, but I do do programming. For example, I am designing/implemententing a programming language ATM. If I were to try to enumerate all the programs that could be written in my language, it would take up more than all the matter in the universe. However that does not stop me from reasoning about it, nor does it dtop my computer from running a compiler and interpreter for that language.
If my language could not be espressed in a finite set of symbols, it couldn't exist in any real sense.
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timeasmymeasure
no subject
Date: 2009-02-20 11:44 pm (UTC)The phrase "uncountably large collections" isn't uncountably large. Your brain is a finite object or finite size and there is a limit to the complexity of the things it can think about. The concept of "uncountably large" is not sich a complex thing.
I don't really do maths, but I do do programming. For example, I am designing/implemententing a programming language ATM. If I were to try to enumerate all the programs that could be written in my language, it would take up more than all the matter in the universe. However that does not stop me from reasoning about it, nor does it dtop my computer from running a compiler and interpreter for that language.
If my language could not be espressed in a finite set of symbols, it couldn't exist in any real sense.