The essence of mathematics lies precisely in its freedom.
Georg CantorRead
A set is a Many that allows itself to be thought of as a One.
Interpretation
This quote highlights the concept of a set as a collective entity while acknowledging its individual elements.
Georg Cantor's quote reminds us that a set, although composed of many distinct elements, can be viewed and treated as a single unified entity. This philosophical insight speaks to the deeper nature of understanding collective groups and their identity, illustrating the balance between individuality and unity in mathematics and beyond.
In practice
In a mathematics lecture discussing the foundational principles of set theory.
The essence of mathematics lies precisely in its freedom.
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.
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.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
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 essence of mathematics lies in its freedom.
Just as a well-filled day brings blessed sleep, so a well-employed life brings a blessed death.
And who ever said the world was fair, little lady? Maybe death is fair, but certainly not life. We must accept the unfairness as proof of the sublime flux of existence, the capricious music of the universe- and go on about our tasks
Make me an instrument of thy peace.
We get into the habit of living before acquiring the habit of thinking.
Fanaticism is at its very strongest when it has political or, better still, religious motivation.
If the provisions of the Constitution be not upheld when they pinch as well as when they comfort, they may as well be abandoned.
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