Channel: Looking Glass Universe

Category: Science & Technology

Tags: lewis carrollmathematicsmathsgodel escher bachinfinitenumbersreal numbers class 10set theorycalculusbrain teaserreal analysiszeno's paradoxnumberzenocomputable numbers infinitymath puzzleanalysis rudinparadoxthe real numberslooking glass universeachillesinfinite seriesrudin real analysismathematical analysisinteresting mathsinteresting mathematicsreal numbersinfinitymathcantor

Description: We usually say that infinity isn't real, but here we'll see how crucial it is to have one very big infinity for the real world; there is an infinite number of numbers. But why do we need real numbers at all? Aren't rational numbers enough? And what about hyperreal numbers? What we'll see in this video is that discovering or defining the real numbers is what allowed calculus to be made rigourous- and without it, we'd need to divide by 0 every time we took a derivative. This video is about the seeming mathematical paradox that arises to get Archilles from A to B (that isn't Zenos paradox!). Check out Nick Lucid's video on whether the universe is infinite: youtu.be/fApKpDGGDYk