Georg Cantor. In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. 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. Georg Cantor quotes The totality of all alephs cannot be conceived as a determinate, well-defined, and also a finished set. This view [of the infinite], which I consider to be the sole correct one, is held by only a few. I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science. Remarkable Last Words (or Near-Last Words). A set is a Many that allows itself to be thought of as a One. Cantor later extended his studies and published a series of six articles ‘Mathematics Annalen’ which contained an introduction to this set theory. 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 essence of mathematics lies in its freedom. I call this the improper infinite [das Uneigentlich-unendliche]. A collection of Georg Cantor Quotes about mathematics, logic, power, conclusion, innovation, people, art, mind, matter, beauty, education, development, numbers, facts, discovery etc. The pure mathematician knows that pure mathematics has an end in itself which is more allied with philosophy. Book by Georg Cantor, 1883. Thus this domain is a definite, actually infinite set of values. "Modern Mathematicians". "Cantor's Grundlagen and the paradoxes of Set Theory". Being a renowned mathematician, he shared his views on various aspects of life including mathematics, research, life, success, failure, etc. 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. Infinity, in its first form (the improper-infinite) presents itself as a variable finite [veranderliches Endliches]; in the other form (which I call the proper infinite [Eigentlich-unendliche]) it appears as a thoroughly determinate [bestimmtes] infinite. 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! Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand! We have collected some of his greatest quotes and sayings below. There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. "Journey Through Genius". My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. Book by Jean van Heijenoort, 1967. Improve yourself, find your inspiration, share with friends. Soon after that he started working on trigonometric series by Bernhard Riemann, a German mathematician and his work later came to be known as the set theory. 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. 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. Book by William Bragg Ewald, 1996. Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number. The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers. He worked there for 10 years and in-between he also published a series of ten papers wherein he mentioned about the theory of numbers. "Communications on the Theory of the Transfinite ('Mitteilungen zur Lehre vom Transfiniten')". Georg Cantor — As quoted in Journey Through Genius (1990) by William Dunham Tags: theory , stands , firm , rock , arrow , directed , against , return , quickly This view [of the infinite], which I consider to be the sole correct one, is held by only a few. The essence of mathematics lies precisely in its freedom. 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. Holding hands at midnight And you can get it if you try. 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. I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

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