In Mathematics, The Art Of

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

A False Conclusion Once Arrived At And Widely Accepted Is Not Easily Dislodged And The Less It Is Understood The More Tenaciously It Is Held.

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.

In Mathematics The Art Of Proposing A Question Must Be Held Of Higher Value Than Solving It.

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.