> My claims in short: 1) most of `elementary mathematics' is not sufficiently > well understood by the mathematical establishment, leading to weaknesses in > K12 and college curriculum, 2) the current theory of `real numbers' is a > joke, and sidesteps the crucial issue of understanding the computational > specification of the continuum, and 3) `infinite sets' are a metaphysical > concept, and unnecessary for correct mathematics.
Here's two relevant quotes:
"ordinary mathematical practice does not require an enigmatic metaphysical universe of sets" (Nik Weaver)
"the actual infinite is not required for the mathematics of the physical world" (Feferman)
Most mathematicians working in the field of foundations understand and accept those quotes, but the average mathematician may not.
What I have suggested is that mathematics needs a reality check; mathematics can and should be treated as a science in which testable consequences are required. I suspect that is what you are getting at, although I don't think you've said it especially clearly.
> Analysts and set theorists are welcome to send me reasoned responses.