ruveyn1

All in favor of throwing the bum off the moving train say Aye. All in favor of putting him off at the next stop say Neigh! Now vote. ruveyn1

Not a -stolen- concept but an idealization. There can only be a countable number of real numbers that can be computed to any desired degree of accuracy. However, that leaves the real number field full of holes unless we assume some property that guarantees local compactness. Most mathematicians prefer a number field that has no holes rather than one in which a Cauchy Sequence does not converge to a member of the field. Being able to take limits makes calculation a lot easier. That is the good news. The bad news might be that physical reality is not locally compact and may be full of holes at the lowest end of resolution. ruveyn1

Not at all. Cutting a reasonable amount of slack for another person is not the same as becoming his doormat. ruveyn1

Our "creator" is nature. So read the DOI as follows: We hold these truths to be self-evident, that all men are by nature equal, that they are endowed by nature with certain inalienable Rights,that among these are Life, Liberty and the pursuit of Happiness. ..... etc. etc.... Most of the Founders were Deists, not Theists. The author of the DOI was in effect a closet atheist. In those days it was not wise to be an explicit atheist in public. In the European nations such a position could end with imprisonment or even capital execution....., ruveyn1

Been there. Done that. I got the t-shirt. I have 4 children and 5 grandchildren. ruveyn1

How many points in the interior of a unit circle? ruveyn1

^ ^ ^ drowning men will grab onto any rope end they can, no matter who owns the rope. Doesn't Ayn Rand make a distinction between emergency situations and normal situations? If a fire suddenly broke (life or death situation) out you would grab the nearest extinguisher whether you owned it or not. ruveyn1

Most likely because they are metabolized and broken down quickly. They are partly assimilated and partly excreted. Substances like Mercury are not metabolized and they are not excreted efficiently either. ruveyn

properly measured physical quantities are how we get at the underlying facts of nature. Anything in natured should be able to be measured, provided we are smart enough to do it and develop the technology to do it. During the Victorian era, a big leap was made in Britain in developing high resolution measuring instruments. Mass producing them. ruveyn1

He was a good person caught in the midst of bad times. He was trying to find work so he could stay alive. He apparently had no malicious intent nor did he damage life and property. In tough times, it makes sense to cut some slack. If some one did that today and he was not a habitual trespasser, just about any court will let him go with a warning and a suspended sentence. ruveyn1

How would one divide the High Seas into private plots? The Seas have to be open to navigation. Since the Seas are not the creation of any human, they are not to be claimed for exclusive use and occupation by anyone. This is not true of river or coastal areas which are dredged and cleared. Their usefulness is maintained by capital investment and labor (dredging is not as easy occupation). And there is the matter of enforcement. How does one divide the Seas into plots that can be enclosed by a barrier or even guarded? ruveyn1

Virtually all of mathematics, ancient and modern rests on set theory, either explicitly or implicitly. It took a long time to recognize how basic and necessary the concept of set is. ruveyn1

Is that just? You never know for sure. Perhaps one lesson is sufficient to wake someone up. Do you wished to be doomed by a single mistake on your part if correction is possible? If not, then you should not be too anxious to doom others. Personally, I prefer to cut someone some slack if there is a reasonable chance of getting his attention. ruveyn1

Newton and Leibniz developed calculus based on the notion of infinitesimals. And infinitesimal is a "number" or "quantity" that is smaller than any real number but is not zero. Bishop Berkley had a field day deriding that notion. He referred to infinitesimals as "the ghosts of departed quantities" The Bishop was a rather good mathematician himself and he wrote a book which sliced and diced the concept of the infinitesimal. There is only one problem. The notion of the infinitesimal gave the right answers even though the concept was not well found by either Newton or Leibniz. In the early and middle 19 th century (around 1840) Cauchy remedied the situation by providing a rigorous definition of limit. With limit one can define continuity of a function and can also define the derivative of a function (its slope at a point) This turns out to be operationally identical to Leibniz dy/dx, the "quotient" of two infinitesimals. Cauchy finally provided a mathematically sound basis for calculus. Now here is the strange thing. Abraham Robinson dealt with the puzzle --- if infinitesimals are nonsense, why did they give the right answers? In 1960 Abraham Robinson finally gave a kosher definition for infinitesimals in his book "Non-Standard Analysis". This involved extending the real number system using a trick of set theory and formal logic to include infinitesimals. Every genuine real number is surrounded (so to speak) by a swarm of extended real numbers that are infinitesimally close. If you have the chops to deal with the mathematical logic and set theory by all means read the book. It is a hard read, but it is mathematically sound and finally put a foundation under Newton and Leibniz approach. ruveyn1

The mathematical point (an abstraction) is pure place, pure location. It does not have any kind of extension. In the original greek Euclid's "definition" of a point translates as "a point is that which has no parts". Σημεῖόν ἐστιν, οὗ μέρος οὐθέν See: http://farside.ph.utexas.edu/euclid/Elements.pdf The interesting thing is that this "definition" is never used in a proof. Not once in the 13 books of Euclid. It is the postulates that make assertions about points that essentially define the points. Ditto for Euclid's "definition" of a line: A line is a length without breadth. Γρaμμὴ δὲ μῆκος ἀπλaτές But the only thing we "know" about lines is stated in the postulates. Postulate 1. To draw a straight line from any point to any point. Postulate 2. To produce a finite straight line continuously in a straight line. Postulate 5. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. and so on. ruveyn1

6 five round clips equals one thirty round clip. What is the problem? Maybe I don't have a sense of justice. ruveyn1

No fraud allowed either. Also contracts freely entered into must be honored, unless a force major intervenes (like a war, earthquake or tsunami). ruveyn1

I agree. Abolishing the compulsory tax loot funded school system resolves the problems. That is not about to happen any time soon, however. ruveyn1

If you get around in a car how do you fill up your gas tank? Do you barter at every service station you stop at? Your mode of operation is most appropriate to a primitive economy with few goods and services traded. ruveyn1

Is this University a private school. If it is private, then the procedures for expulsion are whatever the owners or board of directors decides it is. A student enrolling in such school implicitly accepts the conditions under which can continue attendance. If this is a private school than the students civil rights were not violated. At most, the student can allege a breach of contract. If the school is taxpayer supported, that is an entirely different matter. ruveyn1

You are wishing for a "guardian law" broad enough to permit the formation of private guards whose practices and organization meets some legal standards. Such a private "guard" would have to be accountable to some authority in case wrong doing is alleged. Who or what is that authority? ruveyn1

On of those "breeders" my one day produce a doctor who extends your life when you reach old age. There is an old saying "Do not pee in the water in which you stand. You may have to drink it some day" ruveyn1

Roark did not have the human material to work with. In AS there were enough Heroic Producers or Heroic spirited folks to at least start a partially self sufficient community. This was not the case in TF ruveyn1