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■ Support us on Patreon: / matesmike ■ Channel members: / @matesmike ■ Instagram: @mates.mike ■ Twitter: @mike_mates Since we were little, we have been taught numbers step by step. First the natural numbers, those used for counting. Then the integers, with the negatives. Then the rational numbers, those that can be expressed as a fraction. And then the real numbers, those that cannot, like pi or Euler's number. And then, the complex numbers. As you can see, each set of numbers is inside the next, so the question is clear. Is there any other set that extends all of these numbers? Or to put it another way, are there numbers beyond the real numbers? The answer is yes, there are many more numbers, and in this video we are going to look at one of them, the surreal numbers, an extension of the real numbers that allows us to work with infinite and infinitely small quantities. Hold on tight, because we are going to go to infinity, and much further. 00:00 Introduction 01:00 How numbers are extended 02:56 Surreal numbers 08:24 Infinites and infinitesimals 13:18 Some problems ►► SOME VIDEOS: ► INFINITY SAGA: • The Hotel Paradox with Infinite Numbers... ► FACTORIAL SAGA: • What is the Factorial in Mathematics and... ► THE RIEMANN HYPOTHESIS: • The Pattern of Prime Numbers and the... ► The Order of the Factors DOES alter the Product: • The Order of the Factors DOES alter the... ► How to Divide by 0 Without Collapsing the Universe: • How to Divide by 0 without Breaking the Un... ►Equations and fractals: • How to CREATE FRACTALS with POLYNOMIALS ...