--- title: "Meaning & Key Takeaway of: The difficulties in the study of the…" description: "\"The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those propertie..." image: "https://sms4smile.com/quotes/i/ade/galileo-galilei-2377_arise_the-difficulties-in-the-study-of-the-inf_2755033.png" --- # The difficulties in the study of the infinite arise… ![“The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than…” quote by Galileo Galilei](https://sms4smile.com/quotes/i/ade/galileo-galilei-2377_arise_the-difficulties-in-the-study-of-the-inf_2755033.png) [Download](https://sms4smile.com/quotes/i/ade/galileo-galilei-2377_arise_the-difficulties-in-the-study-of-the-inf_2755033.png) [Open image](https://sms4smile.com/quotes/i/ade/galileo-galilei-2377_arise_the-difficulties-in-the-study-of-the-inf_2755033.png) > “The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.” [Galileo Galilei](https://sms4smile.com/quotes/author/galileo-galilei/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Human attempts to describe infinity using finite concepts are flawed; infinite quantities cannot be compared as greater or less in the same way finite ones are. **In simple terms:** Finite minds misdescribe infinity. Key Takeaway Recognize limits of finite reasoning. Themes philosophy mathematics infinity logic Mood intellectual curious Type academic theoretical When to use this quote - mathematical reasoning - educational curricula - philosophical debate Key Concepts science epistemology theory Questions to Reflect On - How can we responsibly discuss infinities? - What alternative frameworks help? A Different Perspective Infinite concepts may be beyond human comprehension. ★ ★ ★ ★ ★ No ratings yet [Difficulties](https://sms4smile.com/quotes/about/difficulties/) [Education](https://sms4smile.com/quotes/about/education/) [Giving](https://sms4smile.com/quotes/about/giving/) [Mind](https://sms4smile.com/quotes/about/mind/) [Property](https://sms4smile.com/quotes/about/property/) [Psychology](https://sms4smile.com/quotes/about/psychology/) ## Related quotes > [If you stop and you think about everything we hold of value on this planet, metal, minerals, energy, real estate, the things that nations…](https://sms4smile.com/quotes/peter-diamandis/if-you-stop-and-you-think-about-everything-we-hold-of-value-on-this/) [Peter Diamandis](https://sms4smile.com/quotes/author/peter-diamandis/) > [Some people are trapped by the belief that love comes in finite quantities, and that our kind of love exhausts the supply upon which…](https://sms4smile.com/quotes/andrew-solomon/some-people-are-trapped-by-the-belief-that-love-comes-in-finite/) [Andrew Solomon](https://sms4smile.com/quotes/author/andrew-solomon/) > [The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than…](https://sms4smile.com/quotes/georg-cantor/the-potential-infinite-means-nothing-other-than-an-undetermined/) [Georg Cantor](https://sms4smile.com/quotes/author/georg-cantor/) > [Definitions must contain the means of reaching a decision in a finite number off steps, and existence proofs must be conducted so that the…](https://sms4smile.com/quotes/leopold-kronecker/definitions-must-contain-the-means-of-reaching-a-decision-in-a-finite/) [Leopold Kronecker](https://sms4smile.com/quotes/author/leopold-kronecker/) > [My ultimate goal is to create operating systems for myself that allow me to think as little as possible about the silly decisions you…](https://sms4smile.com/quotes/alexa-von-tobel/my-ultimate-goal-is-to-create-operating-systems-for-myself-that-allow/) [Alexa Von Tobel](https://sms4smile.com/quotes/author/alexa-von-tobel/) > [Well, since paradoxes are at hand, let us see how it might be demonstrated that in a finite continuous extension it is not impossible…](https://sms4smile.com/quotes/galileo-galilei/well-since-paradoxes-are-at-hand-let-us-see-how-it-might-be/) [Galileo Galilei](https://sms4smile.com/quotes/author/galileo-galilei/) > [Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are…](https://sms4smile.com/quotes/galileo-galilei/infinities-and-indivisibles-transcend-our-finite-understanding-the/) [Galileo Galilei](https://sms4smile.com/quotes/author/galileo-galilei/) > [War is being declared to-morrow here so perhaps you can understand that I have been working under difficulties, but difficulties negligible compared with what…](https://sms4smile.com/quotes/malcolm-lowry/war-is-being-declared-to-morrow-here-so-perhaps-you-can-understand/) [Malcolm Lowry](https://sms4smile.com/quotes/author/malcolm-lowry/) > [Sincerity and honesty carry one through many difficulties which all the arts he can invent would never help him through.](https://sms4smile.com/quotes/benjamin-stillingfleet/sincerity-and-honesty-carry-one-through-many-difficulties-which-all/) [Benjamin Stillingfleet](https://sms4smile.com/quotes/author/benjamin-stillingfleet/) > [Men are always averse to enterprises in which they foresee difficulties.](https://sms4smile.com/quotes/niccolo-machiavelli/men-are-always-averse-to-enterprises-in-which-they-foresee/) [Niccolo Machiavelli](https://sms4smile.com/quotes/author/niccolo-machiavelli/) > [Lifes difficulties can seem overwhelming, and you may face times when problems seem encompassing. 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