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Re: Non-Euclidean Arithmetic
Posted:
Sep 14, 2012 11:40 AM
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PT II says:
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A proof is a process, especially a constructive proof like the one I gave in
http://mathforum.org/kb/message.jspa?messageID=7889634
of how to construct the location of product ab on the real number line
from being given the locations of 1, a, and b on the real number line,
where a and b are arbitrary reals.
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Oh for heavens sake Paul, you didn't prove anything in any meaningful sense of the word. You described a rather standard construction that illustrates the relationships between line lengths and real number products. If you want to call your describing thereof a "process", I don't care.
But the process we were discussing is supposedly one that takes any two real numbers in general and produces an answer. Any grade school kid knows what that means for small integers: What is 2 times 2? Answer is 4. What is 3 times 7? Answer: "it exists!" -- uh, no, 21; detention for you Johnny. They could even use various processes to get to these answers.
So for this one aspect, and a very important one, there is this vast gulf between multiplication viewed as something that takes two numbers as input and produces a number as output, and real number multiplication for which no such process exists. For other aspects, there is common ground.
Perhaps you should brush up on grade 2 concepts.
Joe N
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