Rational numbers

Posted by on Jun 7, 2013 in Blog, Numbers | 0 comments

Rational numbers

In a previous post, I discussed the basic concept of number, beginning with natural numbers, or counting numbers. I am pursuing a notion here that certain kinds of numbers go together with certain kinds of operation. In the case of the natural numbers, the fundamental operation is counting. We begin with no thing and add one thing to it. The addition is equivalent to a count of one. Intellectually, if we have a set of, say, three items in front of us, and we are going to count them, we begin with nothing (“0”), then count “1”, then “2”, then...

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Maxwell’s Demon and counting

Posted by on Apr 18, 2013 in Blog, Numbers, Science | 0 comments

Maxwell’s Demon and counting

I have already written about Maxwell’s demon in a previous post some time back. Before going on with this post, unless you know the demon well, you should read that previous post. He is a most interesting wee beasty. In the early days of the demon, the notion was that he could decide which molecules had greater or lesser energy, and with this knowledge, decrease the entropy of the system by increasing the temperature of one side of the container and decreasing that of the other. By doing this without any expenditure of work, he violates the second law of thermodynamics. This operation...

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Numbers: sets or successors?

Posted by on Apr 17, 2013 in Blog, Numbers | 0 comments

Numbers: sets or successors?

When I was in high school, I played football. My position was defensive tackle, it’s a rough game; and eventually, I wound up with torn cartilage in my left knee. I had surgery for that when I was sixteen, and recovered quickly. When I got to university a year later, I was a philosophy major. I was reasonably good at math & science, but I didn’t find it very challenging; so philosophy for me. Between my first and second year in that, I picked up a summer job washing cars. All the up & down movement, bending over, and et cetera, re-injured my knee. So, off to hospital for...

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