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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.

Georg Cantor

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.
GEORG CANTOR

Development Examination Ideas Mathematics Obligation Reality
My beautiful proof lies all in ruins.
GEORG CANTOR

Beautiful Evidence Lying Myself Ruin
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.
GEORG CANTOR

Acceptance Easy Fake Undesrtand Wide
To ask the right question is harder than to answer it.
GEORG CANTOR

Answer Hard Question Right
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.
GEORG CANTOR

Definition Development Freedom Mathematics
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!
GEORG CANTOR

Consequence Forever History Logical Possible View
Use Campaign link tagging labels all for specifying slight differences in content for split testing.
GEORG CANTOR

Difference Fault Label
Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
GEORG CANTOR

Consistency Number Science
In mathematics the art of proposing a question must be held of higher value than solving it.
GEORG CANTOR

Art Mathematics Proposal Question Solve Value
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.
GEORG CANTOR

Nature Number Opinion Place View
In mathematics, the art of asking questions is more valuable than solving problems.
GEORG CANTOR

Mathematics Problem Question Value
The transfinite numbers are in a sense the new irrationalities they stand or fall with the finite irrational numbers.
GEORG CANTOR

Fall Mathematics Number Science Stand
Great innovation only happens when people aren’t afraid to do things differently.
GEORG CANTOR

Afraid Different Greatness People
Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!
GEORG CANTOR

Demand Greatness Myself Patience Time
The essence of mathematics lies precisely in its freedom.
GEORG CANTOR

Freedom Lying Mathematics
Don’t always blindly follow guidance and step-by-step instructions; you might run into something interesting.
GEORG CANTOR

Guidance Instruction Interest Run Yourself

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.

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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.

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Popular Authors

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