I was just explaining this to my 6th grade son, and he was extremely confused. I actually think it's cute in a scary "American Education System" way that there are people here arguing that 0.333... = 1/3 is just an approximation for convenience. Just do the opposite; use long division to divide 1 by 3. Just because we can't finish the problem in a finite amount of time doesn't make it an approximation. It is what it is.
There are several proofs for 0.999... = 1, and the some are already here. Math deals with infinity and repeating decimals ALL THE TIME. If 0.333... was just an approximation, all of our upper mathematical theories would just collapse in failure.
And don't even get started with e^(pi*i) + 1 = 0. That might make people's heads explode.
There are several proofs for 0.999... = 1, and the some are already here. Math deals with infinity and repeating decimals ALL THE TIME. If 0.333... was just an approximation, all of our upper mathematical theories would just collapse in failure.
And don't even get started with e^(pi*i) + 1 = 0. That might make people's heads explode.