The essence of mathematics lies precisely in its freedom.
Georg CantorRead
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.
Interpretation
What this quote means
The quote discusses the relationship between variable quantities and the concept of the actual infinite.
Georg Cantor emphasizes the importance of both variable quantities and the concept of the actual infinite in mathematics. He asserts that our reliance on variable quantities implies a necessity for understanding the actual infinite, which relates to notions in set theory and the foundations of mathematics.
Themes
InfinityMathematicsVariable QuantitiesSet TheoryPhilosophy
In practice
Example use cases
This quote can be used in a mathematical seminar discussing the foundations of set theory.
More from Georg Cantor
All quotes βI 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 CantorRead
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 CantorRead
A set is a Many that allows itself to be thought of as a One.
Georg CantorRead
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
Georg CantorRead
The essence of mathematics lies in its freedom.
Georg CantorRead
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