The Essence Of Mathematics Lies Precisely In

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.

Don't Always Blindly Follow Guidance And Step-by-step Instructions; You Might Run Into Something Interesting.

What I Assert And Believe To Have Demonstrated In This And Earlier Works Is That Following The Finite There Is A Transfinite (which One Could Also Call The Supra-finite), That Is An Unbounded Ascending Lader Of Definite Modes, Which By Their Nature Are Not Finite But Infinite, But Which Just Like The Finite Can Be Determined By Well-defined And Distinguishable 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.