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Mathematics
«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.»
Author: Georg Cantor
| About:
Infinity,
Mathematics
| Keywords:
all-around, infinity, inhabits, myopia, sustains
«The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.»
Author: Georg Cantor
| About:
Infinity,
Mathematics
| Keywords:
absolute magnitude, contingent, contingent on, grasps, infinite number, occurs, otherworldly
«The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.»
Author: Georg Cantor
| About:
Infinity,
Mathematics
| Keywords:
delimited, finite, Finite number, infinite number, introducing, irrational, modification, modifications, unconditionally
«Philosophy is written in that great book which ever lies before our eyes ... We cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language ... without whos»
Author: Galileo Galilei
(Astronomer, Mathematician, Philosopher)
| About:
Language,
Mathematics,
Philosophy
| Keywords:
mathematical, symbols
«The dialectic is neither fiction or mysticism, but a science of the forms of our thinking insofar as it is not limited to the daily problems of life but attempts to arrive at an understanding of more complicated and drawn-out processes. The dialectic and formal logic bear a relationship similar to that between higher and lower mathematics.»
«The dialectic is neither fiction nor mysticism, but a science of the forms of our thinking insofar as it is not limited to the daily problems of life but attempts to arrive at an understanding of more complicated and drawn-out processes. The dialectic and formal logic bear a relationship similar to that between higher and lower mathematics.»
«There are things which seem incredible to most men who have not studied mathematics.»
Author: Aristotle
(Philosopher, Physician, Scientist)
| About:
Mathematics
| Keywords:
incredible, studied
«Pure mathematics is, in its way, the poetry of logical ideas.»
Author: Albert Einstein
(Physicist)
| About:
Mathematics
| Keywords:
ideas, logical, poetry, pure, pure mathematics
«Some mathematician has said pleasure lies not in discovering truth, but in seeking it.»
Author: Leo Nikolaevich Tolstoy
(Novelist, Philosopher, Thinker)
| About:
Mathematics,
Pleasure,
Truth
| Keywords:
discovering, seeking