Take it to the limit one more time – a history of calculus I.I

In the previous episode I presented what I have always taken to be Euclid’s proof that there is no greatest prime number, an elegant reduction ad absurdum proof. Over the decades, I must have seen it present as such in at least a dozen different sources, including as an example of a reductio ad absurdum proof, an illustration of the idea. I have never thought to question this. I presented it thus: In The Elements Euclid (fl. 300 BCE) also avoids real infinity presenting only potential infinity. People often refer to his famous proof that there are infinite prime numbers but he doesn’t prove that. Rather, Euclid, in a wonderful reductio ad absurdum proof, merely shows that cannot be a greatest a greatest prime number: We assume there is a greatest prime number P. We then create N the sum of all the prime numbers from 1 to P and add one to the sum: N = (1+2+3+5+7+11…P)+1 This number is not divisible by any prime number, as doing so always leaves a remainder of 1. This means either N is…