非传统音程及其使用。哪些是真正有意义的？
Non-traditional intervals and their use. Which ones really make sense?
摘要：
本文讨论了为什么作为区间分析主要对象的区间具有我们熟知和习惯使用的形式，而不是其他形式的问题。特别是，我们调查为什么传统的时间间隔是封闭的，即，e.包含它们的端点，以及空区间有什么问题。在工作中考虑的第二个问题是如何方便，它是扩大了一些其他对象的传统间隔集。我们表明，不适当的（“反向”）的间隔和算术的间隔（Kaucher完全区间运算）是非常有用的，从许多不同的观点。
英文摘要：
The paper discusses the question of why intervals, which are the main object of Interval Analysis, have exactly the form that we know well and habitually use, and not some other. In particular, we investigate why traditional intervals are closed, i.\,e. contain their endpoints, and also what is wrong with an empty interval. The second question considered in the work is how expedient it is to expand the set of traditional intervals by some other objects. We show that improper ("reversed") intervals and the arithmetic of such intervals (Kaucher complete interval arithmetic) are very useful from many different points of view.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
