[jerf]

"This suggests to me that there is a wider gap between the computables and the reals"

I didn't say "wider". I said more subtle. It doesn't take much mathematical intuition and training to understand the rationals versus the reals. Understanding the computables versus the reals is a lot more tricky and takes a lot more thought. The simple arguments that show the difference between the rationals and the reals require a lot of very careful adjustment if you want to translate them to the computables versus the reals.

I agree the gap up to the reals is still bigger than rational -> computable. The reals are weird. This is a meme but there's a lot of truth in it: https://www.reddit.com/media?url=https%3A%2F%2Fpreview.redd....