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 →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 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
Similar quotes
God's Kingdom is "present in its beginnings, but still future in its fullness. This guards us from an under-realized eschatology (expecting no change now) and an over-realized eschatology (expecting all change now). In this stage, we embrace the reality that while we're not yet what we will be, we're also no longer what we used to be.
Timothy KellerRead
The notion that a radical is one who hates his country is naïve and usually idiotic. He is, more likely, one who likes his country more than the rest of us, and is thus more disturbed than the rest of us when he sees it debauched. He is not a bad citizen turning to crime; he is a good citizen driven to despair.
H. L. MenckenRead
Everywhere is the center of the world. Everything is sacred.
Black ElkRead
I believe in the equality of man; and I believe that religious duties consist in doing justice, loving mercy, and endeavoring to make our fellow-creatures happy.
Thomas PaineRead
We say that the hour of death cannot be forecast, but when we say this we imagine that hour as placed in an obscure and distant future. It never occurs to us that it has any connection with the day already begun or that death could arrive this same afternoon, this afternoon which is so certain and which has every hour filled in advance.
Marcel ProustRead
Our actions are like ships which we may watch set out to sea, and not know when or with what cargo they will return to port.
Iris MurdochRead