Georg Cantor ranks among the greatest of mathematicians and, by implication, philosophers of the nineteenth and twentieth centuries. He gave us the first tangible dimensions for infinities. He moved the realm of infinity, and by extension, eternity, from the exclusive territory of metaphysics and religious philosophy to that of mathematicians and physicists. To him, finding and understanding infinities may have been the beginning to finding and understanding the essence of God. Most mathematicians use symbols based on the Greek alphabet, but Cantor used the first letter of the Hebrew alphabet, “Aleph,” to represent the “beginning” of his defined infinities. Since then, it’s the only commonly used Hebrew letter in mathematics.
Though infinities would seem to contain everything –they do not. Though each infinity continues indefinitely, they are missing elements—the infinites are unique. Each Aleph has a subscript to identify its uniqueness from the other infinites.
\(\aleph_0 \; \text {infinite set of integers}\\ \aleph_1 \; \text{the set of irrational numbers, including transcendental numbers.} \\ . \hspace {1em} \small \text {(There are more irrational numbers between two integers than there are integers).}\\ \aleph_2 \; \text{the set of lines that intersect a point. }\)
An amazing mind, for sure, but it seems that giving birth to great ideas requires a certain amount of travail.
Cantor had his critics and detractors. One of the most notable was Poincare, who declared Cantor’s ideas a "grave disease" infecting the discipline of mathematics, and Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "scientific charlatan," a "renegade" and a "corrupter of youth." Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable. Source: (wikipedia.org/wiki/Georg_Cantor) and ( Joseph Dauben, (2004), "Georg Cantor and the Battle for Transfinite Set Theory")
Cantor seemed stoical about criticism, but he passed it on in kind –actually, he was much better at biting his contemporaries. Cantor opposed the theories of infinitesimals; describing them as both "an abomination" and "a cholera bacillus of mathematics" Cantor also published an erroneous "proof" of the inconsistency of infinitesimals. Apparently, Cantor could understand the infinitely large but not the infinitely small. Source: (wikipedia.org/wiki/Georg_Cantor) and (Nominalistic Tendencies in Contemporary Mathematics and its Historiography", Foundations of Science, 17 (1): 51–89)
I may have found another infinity after reading these technical mathematical publications. Though the information is finite, it might take me an infinite amount time to understand it.
.
