Ackermann functions are used recursively to define the transfinite cardinals of Cantor. Axiom of Monotonicity is defined and used to derive Continuum Hypothesis. Axiom of Fusion is defined and used to split the unit interval into infinitesimals

A set theory called Intuitive Set Theory is introduced in which Skolem Paradox does not appear. A measure function called real measure is defined in which Axiom of Choice cannot produce a nonmeasurable set

Two axioms which define intuitive set theory, Axiom of Combinatorial Sets and Axiom of Infinitesimals, are stated. Generalized Continuum Hypothesis is derived from the first axiom, and the infinitesimal is visualized using the latter

Intuitive set theory is defined as the theory we get when we add the axioms, Monotonicity and Fusion, to ZF theory. Axiom of Monotonicity makes the Continuum Hypothesis true, and the Axiom of Fusion splits the unit interval into infinitesimals