Ars combinatoria ( alphabet of human thought).Vis viva (principle of conservation of energy).Succinct style and polished language - manifested in my legal-writing blog, Disputed Issues - reverse the common limitations besetting brief writers: lack of skill for concision and lack of time for perfection. The second is high polish, achieved by allotting more time to each project than competitors afford. I spurn the unreadable verbosity and stupefying impertinence of ordinary briefs to perform feats of concision and uphold strict relevance to the issues. Some other legal-brief writers research thoroughly and analyze penetratingly, but I bring another two merits. (University of Denver) American Jurisprudence Award in Contract Law Ph.D. jurisdictions.įormer Appellate /Law & Motion Attorney at large Los Angeles law firm J.D. Joshua Tree, California 92252-2141, United States SUPPLIER OF LEGAL THEORIES.Īttorneys' ghostwriter of legal briefs and motion papers, serving all U.S. This argument applies only to those versions positing infinite worlds. Some many-worlds theories do, and some don't. Corrected claim that many-worlds theories of quantum mechanics posit an infinity of worlds. Line segments employing them, must be conceived as actually existing. Many worlds, unlike infinitesimals and the conceptual Infinity any more than does the existence of a line segment, which can beĭecomposed into uncountably many segments, but an infinite plurality of worlds does It’s been argued that some versions of the many-worlds interpretation of quantum mechanics that invoke an uncountable infinity of worlds don't require actual This understanding reinforces the pointĪbout dubious physical theories that posit an It doesn’t automatically subdivide it infinitely, which result would require There’s no limit to how many times you can subdivide the path, but traversing Shown is that the sub-trips are potentially
Zeno’s paradox conceives motion as an actual infinity of sub-trips, but, in reality, all that can be The reason that mathematical infinitiesĪre not just consistent but are useful is that potential infinities canĮxist. That infinitesimals are mathematical fictions solidifies the distinctionīetween actual and potential infinity. The calculus solves the paradox only if actual infinitesimals As we’ve seen,Īctual infinity and infinitesimals are inseparable, certainly where, as here, This context, we treat the infinitesimal as if it were zero.
Leibniz infinitesimals series#
Calculus can be developed in terms of infinitesimals,Īnd in those terms, the series comes infinitesimally close to the limit, and in Series created by adding half the remaining distance, I only approach the limitĮquated with the wall.
Represents an inclusive limit-I actually reach the wall. The expense of logical rigor because it is achieved by ignoring the distinctionīetween exclusive and inclusive limits. Tractable it doesn’t show how it can occur. But the answer only shows that (apparent) motion is mathematically Is pronounced to be that the mathematics of infinite series was yet to be Mathematically, the infinite series of times actually does sum to aįinite value, which equals the time required to walk the distance Zeno’s deficiency Resolved the paradox by refuting the premise that an infinite series can’t beĬompleted.
Standard view holds that the invention of the integral calculus completely
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