4 ms·
And this is why I prefer hyperreals. 0.999... = 1 - 1/∞ We talk about infinity all the time in mathematics, teachers use the concept to introduce calculus in
by calibas 7y ago
And this is why I prefer hyperreals.
0.999... = 1 - 1/∞
We talk about infinity all the time in mathematics, teachers use the concept to introduce calculus in a way that people can more easily understand, but using infinity directly is almost universally banned within classrooms.
Nonstandard analysis is a much more intuitive way of understanding calculus, it's the whole "infinite number of infinitely small pieces" concept, but you're allowed to write it down too.
- __s 7y agoI think what's important here is that if you're making that claim, 0.333... = 1/3 - 1/∞ Which implies 3/∞ = 1/∞
- calibas 7y agoApologies, I should have explained it differently. 0.999... implies a number infinitesimally smaller than 1. You wouldn't use 0.999... in a hyperreal system because you can represent it directly. I shouldn't have mixed different systems and claimed they're mathematically equivalent, you've proven that doesn't work.
- __s 7y agoAgreed, I think the main lesson from this topic is that decimal numbers are a pain. Stick to integers & symbolic operations. You can spit out a decimal approximation at the end Computers agree: never trust precision to floats