In this paper a concept of infinity is described which extrapolates themeasuring properties of number rather thancounting aspects (which lead to cardinal number theory).\udInfinite measuring numbers are part of a coherent number system extending the real numbers, including both infinitely large and infinitely small quantities. A suitable extension is the superreal number system described here; an alternative extension is the hyperreal number field used in non-standard analysis which is also mentioned.\udVarious theorems are proved in careful detail to illustrate that certain properties of infinity which might be considered false in a cardinal sense are true in a measuring sense. Thus cardinal infinity is now only one of a choice of possible extensions of the number concept to the infinite case. It is therefore inappropriate to judge the correctness of intuitions of infinity within a cardinal framework alone, especially those intuitions which relate to measurement rather than one-one correspondence.\udThe same comments apply in general to the analysis of naive intuitions within an extrapolated formal framework.\ud
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机译：在本文中，描述了无穷大的概念，该无穷大的概念外推了数字的主题确定属性，而不是计数方面（这导致基数理论）。\ ud无限量数是扩展实数的相干数系统的一部分，包括无穷大和无穷小数量。合适的扩展是此处描述的超实数系统；另一种扩展是在非标准分析中使用的超实数字段，该字段也被提到。\ ud各种定理经过仔细详细地证明，以说明在基数意义上可能被视为错误的无穷大某些性质在度量意义上是正确的。因此，基数无穷大现在只是数概念可能扩展到无穷大情况的一种选择。因此，仅在一个基本框架内判断无穷直觉的正确性是不合适的，尤其是那些与测量有关而不是一一对应的直觉的正确性。\ ud相同的评论通常适用于在外推形式框架内对朴素直觉的分析。 。\ ud
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