Extremely good insight. An arbitrary real number is essentially a number whose decimal digits are random, in the sense of incompressibility. There is no formula or computer program anyone could ever come up with that can crank out its digits.
By the way note that pi is NOT a random real number in that sense. Its digits are the output of many formulas and algorithms. Pi is a computable real number. Most real numbers are not computable.
I have said no such thing and I believe no such thing. You have made up a claim out of thin air an attributed it to me.
I’m perfectly well aware of modern set theory and the idea of cardinalities. I’m glad you looked it up and perhaps learned something; and if you have any questions about it, I’d be happy to answer them. I’m fully conversant with the theory.
Happy to discuss transfinite set theory. One of my favorite topics. In fact the cardinals are what everyone hears about, but the ordinals are even more interesting. Cantor discovered them too.
By the way, a historical note. What was Cantor doing when he discovered transfinite numbers? Did he wake up one day and say, “I think I’m going to revolutionize the foundations of math, piss off my mentor Kronecker, and have a nervous breakdown?”
No in fact that’s not what happened. Cantor was engaged in studying trigonometric series, the very series that arose from Fourier’s research into heat. In other words Cantor was led to discover transfinite cardinals and ordinals based on problems that arose directly from physical phenomena. Something to think about when contemplating the philosophy of the infinite.
Finally, again reiterating what I said earlier, the statement you attributed to me is NOTHING I said. Nothing at all. You just made it up then pretended to debunk it. I believe in the philosophy biz that’s called a strawman argument.