What I Assert And Believe To Have

Had Mittag-leffler Had His Way, I Should Have To Wait Until The Year 1984, Which To Me Seemed Too Great A Demand!

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, 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.

There Is No Doubt That We Cannot Do Without Variable Quantities In The Sense Of The Potential Infinite. But From This Very Fact The Necessity Of The Actual Infinite Can Be Demonstrated.

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.