I love Ideas

In the past years I learned there is nothing more enjoyable for me than ideas. Since I think that Math is the science of ideas, I would like to share the following proof: Maybe you have heard of prime numbers. These are natural numbers greater than one and only divisible by one and themselves, so 2 is prime, also 3 and 5,7,11, ... Well, how long does it go on after the "..."? Infinitely long! A Greek mathematician called Euclid, who lived around 300 BC, showed this the following way. Let's say there is just a finite number of primes. If we multiply them and add one, we get a new number, let's call it x. x can either be prime or not. If x is prime we have found a number, which is not in our prime number set, which was therefore not complete. If x is not prime, there is a number y, which divides x. But y isn't in our prime number set, because no number in this set can divide x. So also in this case the set wasn't complete. Since we can do this for any finite number of primes, there has to be an infinite number of them ... TADA! (or how we mathematicians say: QED)


Anonymous
Vienna, Austria

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