These number systems already exist, I’m not just making them up.
If someone says 0.666…7 then you have a couple different ways you can take the discussion. You can say, “No! Real numbers don’t work like that!” or you can talk about what number systems would look like if you can do that.
It turns out that there’s a lot to learn from the alternative number systems, including formulations of calculus without limits that are easier to understand from an intuitive perspective, yet equally rigorous. The field is called “nonstandard analysis”. It’s not taught in college.
If someone says 0.666…7 then you have a couple different ways you can take the discussion. You can say, “No! Real numbers don’t work like that!” or you can talk about what number systems would look like if you can do that.
It turns out that there’s a lot to learn from the alternative number systems, including formulations of calculus without limits that are easier to understand from an intuitive perspective, yet equally rigorous. The field is called “nonstandard analysis”. It’s not taught in college.