I think a big issue with how we teach math, is the casualness with which we introduce children to floating points.
Its like: Hey little Bobby, now that you can count here are the ints and multiplication/division. For the rest of your life there will be things to learn about them and their algebra.
Tomorrow we'll learn how to put a ".25" behind it. Nothing serious. Just adds multiple different types of infinities with profound impact on exactness and computability, which you have yet to learn about. But it lets you write 1/4 without a fraction which means its simple!
Totally agree. It bothered me when I was younger, though I had no idea how to explain why, but this should be deeply unsettling to everyone who encounters it:
Its like: Hey little Bobby, now that you can count here are the ints and multiplication/division. For the rest of your life there will be things to learn about them and their algebra.
Tomorrow we'll learn how to put a ".25" behind it. Nothing serious. Just adds multiple different types of infinities with profound impact on exactness and computability, which you have yet to learn about. But it lets you write 1/4 without a fraction which means its simple!