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In mathematics, the art of asking questions is more valuable than solving problems.

Georg Cantor

The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.
GEORG CANTOR

Assumption Determination Limitation Potential Quantity
Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
GEORG CANTOR

Consistency Number Science
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
In mathematics, the art of asking questions is more valuable than solving problems.
GEORG CANTOR

Mathematics Problem Question Value
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.
GEORG CANTOR

Demonstration Doubt Fact Necessary Potential Variable
My beautiful proof lies all in ruins.
GEORG CANTOR

Beautiful Evidence Lying Myself Ruin
A set is a Many that allows itself to be thought of as a One.
GEORG CANTOR

Allow Oneself Thinking
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.
GEORG CANTOR

Destroy Fear High Infinity Mindset Ourselves Possible Secondary
The essence of mathematics lies precisely in its freedom.
GEORG CANTOR

Freedom Lying Mathematics
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
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 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.
GEORG CANTOR

Diversity Doubt Myself Recognition Science Truth
Great innovation only happens when people aren’t afraid to do things differently.
GEORG CANTOR

Afraid Different Greatness People
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
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
To ask the right question is harder than to answer it.
GEORG CANTOR

Answer Hard Question Right

In mathematics, the art of asking questions is more valuable than solving problems.

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In mathematics, the art of asking questions is more valuable than solving problems.

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