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Different levels of infinity in Torah and Mathematics
Saks, TV. 2002.  BH 13:113-120. CELD ID 21433

In this paper, we shall use mathematical infinity to clarify the concept of infinity as discussed in Torah. The concept of infinity is used in Torah in two fundamentally different ways. First, G-d is referred to as Ain Sof, literally, Without End, or Infinite. On the other hand, the Torah has revealed the fact that the creation is infinite (Talmud Hagiga, many references in Hasidism and Kabbala). For example, G-d created infinitely many spiritual worlds, and infinitely many troops of hosts that serve Him. Now surely the concept of infinity as it relates to and describes the creation is vastly inferior to the concept of Infinity as it applies to G-d Himself. In fact, all of G-d's infinitely many troops are considered as absolutely nothing before Him. How can infinity be limited? The modern theory of mathematical infinity, first introduced by G. Cantor in the 1870s, provides a useful framework to describe both a concept of infinity that actually exists and is limited (the created universe), and a qualitatively higher concept of Infinity which is unlimited. The mechanisms which mathematics uses to distinguish between different levels of infinity will be discussed, and a fundamental theorem will be proven. Mathematical infinity is a powerful example of science clarifying a deep concept in Torah, and of science supporting a controversial Torah statement about the creation.