This really benefits from a picture. Calling something “a nonstandard number” doesn’t really convey anything about them and a better name I’ll use is “infinitely big”, because they are.
< makes sense because the 2 chains are finite numbers and infinitely big numbers and an infinitely big number is bigger than any finite one because it’s , well, infinite. I can elaborate more technically, but I think trying to develop some numeracy for infinite numbers is a lot like learning about negatives and rationals and complex numbers. Just play with some expressions and get used to them. then look at the more technical treatment even if you have the ability to read it. Someone gave that example with a flat list but I think and feel that tapping into one’s existing NUMBER (and not list) sense is very powerful since it’s the first math we learn and the only one people use every single day.
This really benefits from a picture. Calling something “a nonstandard number” doesn’t really convey anything about them and a better name I’ll use is “infinitely big”, because they are.
< makes sense because the 2 chains are finite numbers and infinitely big numbers and an infinitely big number is bigger than any finite one because it’s , well, infinite. I can elaborate more technically, but I think trying to develop some numeracy for infinite numbers is a lot like learning about negatives and rationals and complex numbers. Just play with some expressions and get used to them. then look at the more technical treatment even if you have the ability to read it. Someone gave that example with a flat list but I think and feel that tapping into one’s existing NUMBER (and not list) sense is very powerful since it’s the first math we learn and the only one people use every single day.