To Ask The Right Question

Mathematics, In The Development Of Its Ideas, Has Only To Take Account Of The Immanent Reality Of Its Concepts And Has Absolutely No Obligation To Examine Their Transient Reality.

Every Transfinite Consistent Multiplicity, That Is, Every Transfinite Set, Must Have A Definite Aleph As Its Cardinal Number.

I Entertain No Doubts As To The Truths Of The Tranfinites, Which I Recognized With God's Help And Which, In Their Diversity, I Have Studied For More Than Twenty Years; Every Year, And Almost Every Day Brings Me Further In This Science.

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.

The Transfinite Numbers Are In A Sense The New Irrationalities [ ... They] Stand Or Fall With The Finite Irrational Numbers.