To Ask The Right Question Is Harder

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

The Old And Oft-repeated Proposition "totum Est Majus Sua Parte" [the Whole Is Larger Than The Part] May Be Applied Without Proof Only In The Case Of Entities That Are Based Upon Whole And Part; Then And Only Then Is It An Undeniable Consequence Of The Concepts "totum" And "pars". Unfortunately, However, This "axiom" Is Used Innumerably Often Without Any Basis And In Neglect Of The Necessary Distinction Between "reality" And "quantity", On The One Hand, And "number" And "set", On The Other, Precisely In The Sense In Which It Is Generally False.

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.

Great Innovation Only Happens When People Aren't Afraid To Do Things Differently.

The Fear Of Infinity Is A Form Of Myopia That Destroys The Possibility Of Seeing The Actual Infinite, Even Though It In Its Highest Form Has Created And Sustains Us, And In Its Secondary Transfinite Forms Occurs All Around Us And Even Inhabits Our Minds.