To Ask The Right Question Is Harder

Mathematics Is Entirely Free In Its Development, And Its Concepts Are Only Linked By The Necessity Of Being Consistent, And Are Co-ordinated With Concepts Introduced Previously By Means Of Precise Definitions.

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.

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.

My Theory Stands As Firm As A Rock; Every Arrow Directed Against It Will Return Quickly To Its Archer. How Do I Know This? Because I Have Studied It From All Sides For Many Years; Because I Have Examined All Objections Which Have Ever Been Made Against The Infinite Numbers; And Above All Because I Have Followed Its Roots, So To Speak, To The First Infallible Cause Of All Created Things.

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