科技文献中4个不等二元关系符号的左边元素缺失及相关问题

Missing Elements on the Left Side of Four Unequal Binary Relation Symbols and Related Problems in Scientific Literature

探讨科技文献中用于比较实数(或同一类量)大小的不等二元关系符号(≥,≤,>,<)的左边元素(指实数或同一类量)缺失是否产生错误以及主要相关问题,其中同一类量指的是可以相互比较的物理量。根据数学基础知识论证了一个非空集合X上的二元关系符号R的左右两边元素缺一不可的结论,指出了关系符号用法上的注意问题;利用数学知识和国家标准相结合的方法,判定了二元关系符号(≥,≤,>,<)左边元素缺失是错误的,分析了产生错误的原因,给出了纠错方法;结合实例阐明了二元关系符号(≥,≤,>,<)用于变量范围表示时容易误判为关系符号左边元素缺失但实际并不缺失的问题。

It was explored that the potential errors and their main related problems arise from the missing elements—namely,the real number or quantities of the same class—on the left side of binary relation symbols—≥,≤,<or>—in the scientific literature.The quantities of the same class refer to physical quantities that can be compared with each other.Based on fundamental mathematical principles,it was demonstrated that not a single one of the comparable elements on both the left and right side of a binary relation symbol R on a non-empty set X can be omitted,and the problems in the usage of relation symbols were also highlighted.By combining mathematical knowledge and the national standards,it was determined that the missing element on the left sides of the binary relation symbols—≥,≤,<or>—is an error.Through thorough analysis of the reasons behind this error,methods of correcting the error was provided.Combining with the examples,it was clarified that the element(s)on the left side of the binary relation symbols—≥,≤,<or>—is easy to be misjudged as missing but not actually missing when they are used for variable range representation.