Mathematical objects | Infinity | Philosophy of mathematics
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets. Among the axioms of Zermelo–Fraenkel set theory, on which most of modern mathematics can be developed, is the axiom of infinity, which guarantees the existence of infinite sets. The mathematical concept of infinity and the manipulation of infinite sets are used everywhere in mathematics, even in areas such as combinatorics that may seem to have nothing to do with them. For example, Wiles's proof of Fermat's Last Theorem implicitly relies on the existence of very large infinite sets for solving a long-standing problem that is stated in terms of elementary arithmetic. In physics and cosmology, whether the Universe is spatially infinite is an open question. (Wikipedia).
Can You Define the Immeasurable?
What is infinity? Can you define something that, by definition, has no boundaries? A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity still stands as an enigma of the intellectual world. We asked people from all walks of
From playlist Mathematics
Definition of infinity In this video, I define the concept of infinity (as used in analysis), and explain what it means for sup(S) to be infinity. In particular, the least upper bound property becomes very elegant to write down. Check out my real numbers playlist: https://www.youtube.co
From playlist Real Numbers
What’s the biggest number you can think of? Well, what about one more than that number? We can’t really comprehend the idea of infinity, but it’s still a useful concept in science. Brian Greene explains more. Subscribe to our YouTube Channel for all the latest from World Science U. Visit
From playlist Science Unplugged: Physics
It's a concept which intrigues mathematicians, but scientists aren't so keen on it. More at http://www.sixtysymbols.com/
From playlist From Sixty Symbols
This video provides a description of infinity with several examples. http://mathispower4u.com
From playlist Linear Inequalities in One Variable Solving Linear Inequalities
A subject extensively studied by philosophers, mathematicians, and now recently, physicists, infinity is a uniquely universal enigma within the academic world. Thinkers clash over questions such as: Does infinity exist? What types of infinity are there? Watch the Full Program Here: https:
From playlist Mathematics
How many kinds of infinity are there?
A lot. List with links: http://vihart.com/how-many-kinds-of-infinity-are-there/
From playlist Doodling in Math and more | Math for fun and glory | Khan Academy
Infinity: The Science of Endless
"The infinite! No other question has ever moved so profoundly the spirit of man," said David Hilbert, one of the most influential mathematicians of the 19th century. A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity stil
From playlist Explore the World Science Festival
Infinite Limits With Equal Exponents (Calculus)
#Calculus #Math #Engineering #tiktok #NicholasGKK #shorts
From playlist Calculus
How to Find the Limit at Infinity (NancyPi)
MIT grad shows how to find the limit as x approaches infinity or negative infinity. To skip ahead: 1) For a POLYNOMIAL or CONSTANT in the limit expression, skip to 1:56. 2) For a RATIONAL ("FRACTION") expression in the limit, skip to 8:49. 3) For something of the form (SINX)/X, skip to 23:
From playlist Calculus: Limits
Calculus AB Homework 1.4 Limits Involving Infinity
Download Packet: https://goo.gl/WYGSii ================================= AP Calculus AB / IB Math SL Unit 1: Limits and Continuity Lesson 4: Limits Involving Infinity =================================
From playlist AP Calculus AB
Why is infinity not a real number? - Week 2 - Lecture 8 - Mooculus
Subscribe at http://www.youtube.com/kisonecat
From playlist Ohio State: Jim Fowler's Calculus One Lectures | CosmoLearning Mathematics
Charles Rezk - 4/4 Higher Topos Theory
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart4.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
What is Infinity Over Infinity? #SoME2
What is Infinity Over Infinity? ~ This video is my submission for 3Blue1Brown's 2022 SoME2 math content-making competition. In this video I discuss the concept of infinity, limits and end behavior, Cantor's Diagonal Argument and multiple-size infinities, and L'Hopital's rule. I discuss thi
From playlist Summer of Math Exposition 2 videos
The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories - Emily Riehl
Vladimir Voevodsky Memorial Conference Topic: The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories Speaker: Emily Riehl Affiliation: Johns Hopkins University Date: September 12, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Indeterminate Forms In this video, I introduce the concept of indeterminate forms and explain why it is necessary to even have calculus. Then, I go over the main forms, all while emphasizing that in each of them, there is a tug-of-war situation going on. Enjoy! Check out my Calculus Play
From playlist Calculus
To check out the physics courses that I mentioned (many of which are free!) and to support this channel, go to https://brilliant.org/Sabine/ and create your Brilliant account. The first 200 will get 20% off the annual premium subscription. Correction: At 4 mins 44 seconds, it should be t
From playlist Philosophy of Science
Yonatan Harpaz - New perspectives in hermitian K-theory I
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Calculus 2.6 Limits at Infinity
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
What happens to limits at infinity. We also look at one of the uses of limits: continuity.
From playlist Life Science Math: Limits in calculus