List of Georg Cantor Quotes

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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.

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

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

I Realize That In This Undertaking I Place Myself In A Certain Opposition To Views Widely Held Concerning The Mathematical Infinite And To Opinions Frequently Defended On The Nature Of Numbers.

The Transfinite Numbers Are In A Certain Sense Themselves New Irrationalities And In Fact In My Opinion The Best Method Of Defining The Finite Irrational Numbers Is Wholly Disimilar To, And I Might Even Say In Priciple The Same As, My Method Described Above Of Introducing Trasfinite Numbers. One Can Say Unconditionally: The Transfinite Numbers Stand Or Fall With The Finite Irrational Numbers; They Are Like Each Other In Their Innermost Being; For The Former Like The Latter Are Definite Delimited Forms Or Modifications Of The Actual Infinite.

This View [of The Infinite], Which I Consider To Be The Sole Correct One, Is Held By Only A Few. While Possibly I Am The Very First In History To Take This Position So Explicitly, With All Of Its Logical Consequences, I Know For Sure That I Shall Not Be The Last!

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.

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

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 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.