Georg Cantor citáty

Georg Cantor foto
1  0

Georg Cantor

Dátum narodenia: 3. marec 1845
Dátum úmrtia: 6. január 1918

Reklama

Georg Ferdinand Ludwig Philipp Cantor bol nemecký matematik, známy ako tvorca modernej teórie množín. Medzi matematikmi je známy rozšírením teórie množín o koncept transifinitných čísel, vrátane triedy kardinálnych a ordinálnych čísel. Cantor je takisto známy prácou na jedinečnej reprezentácii funkcií pomocou trigonometrických radov .

Podobní autori

 Archimedes foto
Archimedes2
grécky matematik, fyzik, inžinier, vynálezca a astronóm
Carl Friedrich Gauß foto
Carl Friedrich Gauß5
nemecký matematik a fyzikálny vedec
Alexander Graham Bell foto
Alexander Graham Bell1
vedec a vynálezca známy pre jeho prácu na telefóne
Nikola Tesla foto
Nikola Tesla1
srbský americký vynálezca
Henry Ford foto
Henry Ford60
americký priemyselník
Blaise Pascal foto
Blaise Pascal134
francúzsky matematik, fyzik, vynálezca, spisovateľ a kres...
Benjamin Franklin foto
Benjamin Franklin140
americký autor, politický teoretik, politik, vedúci pošty...
Albert Einstein foto
Albert Einstein208
nemecko-americký fyzik a zakladateľ teórie relativity
Thomas Alva Edison foto
Thomas Alva Edison31
americký vynálezca a podnikateľ
Pierre-Augustin de Beaumarchais foto
Pierre-Augustin de Beaumarchais21
francúzsky dramatik a diplomat, vševed

Citáty Georg Cantor

„My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer.“

— Georg Cantor
Context: My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things. As quoted in Journey Through Genius (1990) by William Dunham

Reklama

„The transfinite numbers are in a certain sense themselves new irrationalities“

— Georg Cantor
Context: 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 dissimilar to, and I might even say in principle the same as, my method described above of introducing transfinite 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. As quoted in Understanding the Infinite (1994) by Shaughan Lavine

„The totality of all alephs cannot be conceived as a determinate, well-defined, and also a finished set.“

— Georg Cantor
Context: The totality of all alephs cannot be conceived as a determinate, well-defined, and also a finished set. This is the punctum saliens, and I venture to say that this completely certain theorem, provable rigorously from the definition of the totality of all alephs, is the most important and noblest theorem of set theory. One must only understand the expression "finished" correctly. I say of a set that it can be thought of as finished (and call such a set, if it contains infinitely many elements, "transfinite" or "suprafinite") if it is possible without contradiction (as can be done with finite sets) to think of all its elements as existing together, and to think of the set itself as a compounded thing for itself; or (in other words) if it is possible to imagine the set as actually existing with the totality of its elements. Letter to David Hilbert (2 October 1897)

„I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God.“

— Georg Cantor
Context: I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God. I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures. As quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by Rosemary Schmalz.

„I call this the improper infinite“

— Georg Cantor
Context: As for the mathematical infinite, to the extent that it has found a justified application in science and contributed to its usefulness, it seems to me that it has hitherto appeared principally in the role of a variable quantity, which either grows beyond all bounds or diminishes to any desired minuteness, but always remains finite. I call this the improper infinite [das Uneigentlich-unendliche].

„Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established.“

— Georg Cantor
Context: Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real.

„This view [of the infinite], which I consider to be the sole correct one, is held by only a few.“

— Georg Cantor
Context: This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last! As quoted in Journey Through Genius (1990) by William Dunham ~

Reklama
Reklama
Ďalší
Dnešné výročie
Arthur Schopenhauer foto
Arthur Schopenhauer85
nemecký filozof 1788 - 1860
August Bebel foto
August Bebel13
nemecký sociálny demokrat, politik 1840 - 1913
Sydney Smith foto
Sydney Smith2
anglický spisovateľ a kňaz 1771 - 1845
Andy Warhol foto
Andy Warhol8
americký maliar, filmový tvorca<br />a dôležitá osobnosť ... 1928 - 1987
Ďalších 26 dnešných výročie
Podobní autori
 Archimedes foto
Archimedes2
grécky matematik, fyzik, inžinier, vynálezca a astronóm
Carl Friedrich Gauß foto
Carl Friedrich Gauß5
nemecký matematik a fyzikálny vedec
Alexander Graham Bell foto
Alexander Graham Bell1
vedec a vynálezca známy pre jeho prácu na telefóne
Nikola Tesla foto
Nikola Tesla1
srbský americký vynálezca
Henry Ford foto
Henry Ford60
americký priemyselník