Georg Cantor
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"Georg Ferdinand Ludwig Philipp Cantor" was a Germans/German mathematician, best known as the inventor of set theory, which has become a foundations of mathematics/fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite set/infinite and well-order/well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal number/cardinal and ordinal number/ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.

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Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.

A set is a Many that allows itself to be thought of as a One.

In mathematics the art of asking questions is more valuable than solving problems.

The essence of mathematics lies in its freedom.

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.

One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

In mathematics the art of proposing a question must be held of higher value than solving it.

What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.