🗑️ 🧵 The Case for Real Numbers

Anonymous at Sat, 8 Jun 2024 18:22:27 UTC No. 16222457

Son, we live in a world of mathematical principles, and those principles have to be understood by men who use real numbers. Who's gonna do it. You? You Professor Wildberger? Real numbers have a purpose greater than you can POSSIBLY fathom. You weep for John Gabriel and you curse real numbers. You have that luxury. You have the luxury of not grasping, that the use of real numbers, while confounding, PROBABLY saves time from vapid toiling. And their existence, while grotesque, and incomprehensible to you, saves time.

You don't want to ignore real numbers because deep down in places you don't talk about at conferences, you WANT infinite precision, you NEED infinite precision.

We use concepts like "infinity," "irrationality," "convergence." We use these concepts to understand the universe. You use them as fodder for your skepticism.

I have neither the time, nor the inclination to explain myself to a foundationalist who rises and sleeps under the blanket of the very freedom real numbers and limits provide and then QUESTIONS THE MANNER IN WHICH THEY PROVIDE IT. I would rather you just said THANK YOU, and went on your way. Otherwise I suggest you grab a Cauchy sequence, and take its limit. Either way, I don't give a DAMN, WHAT YOU THINK YOU ARE ENTITLED TO