reals

In other words, having no constructive method for generating the reals is not at all the same thing, of course, as having a proof that the reals are uncountable.

The Lebesgue measure is implied on the Reals if none is given, and the computable reals have measure zero.

The reals one defines thee reals constructively in essentially the same way as one does classically.

The reals are uncountable, ergo there is no constructive method for generating the reals.

The proof that the cardinality of the reals is non-countable is perfectly constructive, see [1] for a discussion of these and related issues.

This is actually a very intuitive argument for why the reals (oops I mean decimals) are not countable.

You will inevitably find that the definable real numbers, like the computable reals, appear to be countable.

So the fact that the computable reals and the definable reals appear countable, is, at least to me, much like the statement that there are countable models of your favorite formal system.

You need to be very, very careful when talking about the size of the constructive reals.

If you're going to work with Cauchy sequences, why bother defining the reals as Dedekind cuts?

He does go on to explain diagonalization, which is of course a better way to demonstrate the uncountability of the reals.

Well, leave out succession and you get the reals, which are still complex enough (no pun intended) to offer hours of fun.

I understand under "constructive reals" the computable reals, and there are only countably many of them.

And the "refutation" of Cantor's argument of the reals is fun too.

By way of providing some hopefully constructive feedback, the language seems a bit excessively informal: "Safe Rust is For Reals Totally Safe.

I suppose it all boils down to how you define "arithmetic", but what is it that the integers have that the reals lack under the relevant definition?