Bamboozled at a young age

i think this is a fairly reasonable gut reaction to first hearing about the "unnatural" numbers, especially considering the ways they're (typically) presented at first. it seems like kids tend to be introduced to the negative numbers by people saying things like "hey we can talk about numbers that are less 0, heres how you do arithmetic on them, be sure to remember all these rules". and when presented like that, it just seems like a bunch of new arbitrary rules that need to be memorized, for seemingly no reason.

i think there would be a lot less resistance if it was explained in a more narrative way that explained why the new numbers are useful and worth learning about. e.g.,

• negative numbers were invented to make it possible to subtract any two whole numbers (so that it's possible to consistently undo addition).
• rational numbers were invented to make it possible to divide any two whole numbers (so that it's possible to consistently undo multiplication, with 0 being a weird edge-case).
• real numbers were invented to facilitate handling geometrical problems (hypotenuse of a triangle, and π for dealing with circles), and to facilitate the study of calculus (i.e. so that you can take supremums, limits, etc)
• complex numbers were invented to make it possible to consistently solve polynomial equations (fundamental theorem of algebra), and to better handle rotations in 2d space (stuff like Euler's formula)

i think the approach above makes the addition of these new types of numbers seem a lot more reasonable, because it justifies the creation of all the various types of numbers by basically saying "there weren't enough numbers in the last number system we were using, and that made it a lot harder to do certain things"