> However, it has the advantage, for beginners, of being very close to the picture of real numbers they already have. Haha, no. And here's why. > Because of i

> However, it has the advantage, for beginners, of being very close to the picture of real numbers they already have. Haha, no. And here's why. > Because of irritating difficulties such as the need to carry digits and to identify 0.999999.... with 1 Not only does this not fit in with people's existing picture of real numbers, people become emotionally attached to the opposite with a fervor unknown in any other part of mathematics! (Second place would be Cantor's theorem for real numbers, but you have to know a little more to be passionately opposed to that.) I think even for beginners who are willing to believe that 0.99999... = 1, they are going to have trouble agreeing that 0.99999... < 1 is a false statement.