>>13430872>gives a map between coding and mathematicsyes proofs are essentially programs
>Your claim was that the idea of pi proves that infinite sets exist somehowNot necessarily, but it was a way to get you to understand what people mean by the idea of infinity, especially in math.
>My reply to that is that to define pi in a way in which you can even make sense to speak of its digits with arbitrary precisionOkay, fine, the loop will never end. Therefore pi is infinite. But my point is this is a backwards way of thinking, because I made the program in the first place because I wanted to represent the algorithm for pi. I have an intuition of an idea, and then I make a formal system or program to represent that idea.
>You may have a definition of pi based on idealized "perfect circles"Yes, its an algorithm that never ends because pi is an infinite real number.
I dont understand your point, what is wrong with assigning a collection of objects a size that is defined as larger then any finite collection. This clearly meets our intuition of infinity, we reason with the concept all the time (think coding, eternal universe etc.), why is the idea suddenly off limits to so many people when it comes to math?
