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merjet last won the day on August 5 2018

merjet had the most liked content!

About merjet

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  1. Thanks. Does employer-employer mean or include customer-supplier, e.g. when a supplier fulfills specs previously given by the customer? Does employee-employee mean or include teamwork, e.g. each one doing different things with the same end goal?
  2. The title of your Chapter 4, collaboration, intrigued me. Using Amazon's "Look Inside" feature, I can see collaboration types 1, 2, and 8. Will you tell us what 3-7 are, at least the labels?
  3. My perspective was whether or not a number was the ratio of two integers, or is equivalent to such a ratio. It either is or isn't. The lengths of the sides of the two are not different in kind in that they are both real numbers, if that's what you mean. And, of course, we can't measure lengths with unlimited precision. Any measurement we express in digits is equivalent to a rational number, e.g. the diagonal of a 1-inch square is 1.41421356237 with 12-digit precision. 1.41421356237 = 141421356237/100000000000
  4. Decimal expansions in base 7 would still include finite, infinite non-recurring, and infinite recurring instances. If by "actual quantities in reality" you mean the result of a measurement, then the result is a matter of precision, i.e. how many significant digits. I doubt there is any mathematician who would say that rational and irrational numbers designate are not different in kind.
  5. The Wright Brothers #1 The Wright Brothers #2 The Wright Brothers #3
  6. Hi Russell, If and when you do move, you might contact Anu Seppala at ARI. She gave me contacts for two couples in the Cleveland area who registered for OCON 2019.
  7. P.S. That should be finite and recurring. That should be non-finite and non-recurring.
  8. Thanks for the reference to Kitcher. I read that book many years ago, but not recently and before I wrote the blog posts. On page 211 Kitcher says: “By contrast, because he cleaves to the intuitive idea that a set must be bigger than any of its proper subsets, Bolzano is unable to define even an order relation between infinite sets. The root of the problem is that, since he is forced to give up the thesis that the existence of one-to-one correspondence suffices for identity of cardinality, Bolzano has no way to compare infinite sets with different members. Second, Cantor’s work yields a new perspective on an old subject: we have recognized the importance of one-to-one correspondence to cardinality; we have appreciated the difference between cardinal and ordinal numbers; we have recognized the special features of the ordering of natural numbers. But we do not even need to go so far into transfinite arithmetic to receive explanatory dividends. Cantor’s initial results on the denumerability of the rationals and algebraic numbers, and the nondenumerability of the reals, provide us with a new understanding of the difference between the real numbers and the algebraic numbers.” In my view Kitcher’s view is rather one-sided, favoring Cantor’s ideas over Bolzano’s. “Bolzano is unable to define even an order relation between infinite sets.” Why not? While the proper subset method is unable to give an order relation between all infinite sets, it is able to give an order relation between some infinite sets. An example of the former is the rationals in the interval [0,2] and the reals in the interval [0,1]. An example of the latter is the integers and reals. It seems Kitcher values the denumerability/nondenumerability criteria much more than I do. According to Cantor, the rationals are denumerable, but the reals are not. On the other hand, comparing the rational numbers to the reals can also be done on the criteria of decimal expansions. We know that rational numbers have finite or recurring decimals expansions and irrational numbers have non-finite or non-recurring decimals. Stephen, I’m sure you know this, but I will give examples for other readers who might not. Rational number examples: 2/7 = 0.2857142857142857….. infinite, recurring 3/10 = 0.3 finite 77238/100000 = 0.77238 finite Irrational number examples: sqrt(2) =1.414213562373095….. infinite, nonrecurring pi = 3.1415926535897932384…. infinite, nonrecurring Starting with any rational number with a finite decimal expansion, one could generate an unlimited number of partly irrational numbers by appending digits randomly (nonrecurring) on the right side. I believe that is as sound or more sound than Cantor’s diagonal argument for real numbers (link).
  9. Infinity contra-Cantor #1Infinity contra-Cantor #2Approaching Infinity
  10. Producers. There are traders who only buy and sell, for example, on a commodities exchange. They may buy and sell pork bellies, corn, wheat, etc. without ever producing those things. If farmers didn't produce those things, the traders couldn't buy and sell them.
  11. China From Above Information and Investment #1 Information and Investment #2 Information and Investment #3 Information and Investment #4
  12. Modern Austrian Economics #3 Modern Austrian Economics #4 Modern Austrian Economics #5 Maximum size of animals Few, several, many, and some The Organization of Industry #1 The Organization of Industry #2 Perfect Competition #1 Perfect Competition #2 Perfect Competition #3 Amazon HQ2 & HQ3 #1 Amazon HQ2 & HQ3 #2 Amazon HQ2 & HQ3 #3 Bohemian Rhapsody Mass shootings
  13. Modern Austrian Economics #1 Modern Austrian Economics #2
  14. Two Kinds of AprioriAccountable Capitalism ActRothbard on Economic Paradigms
  15. Yes, Book IV, Chapter XX.5 http://enlightenment.supersaturated.com/johnlocke/longcontents.html
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