They said its the same number though, not basically the same. The idea that as you keep adding 9s to 0.9 you reduce the difference, an infinite amount of 9s yields an infinitely small difference (i.e. no difference) seems sound to me. I think they’re spot on.
That’s what it means, though. For the function y=x, the limit as x approaches 1, y = 1. This is exactly what the comment of 0.99999… = 1 means. The difference is infinitely small. Infinitely small is zero. The difference is zero.
It’s so dumb and it makes perfect sense at the same time. There is an infinitely small difference between the two numbers so it’s the same number.
No, it’s not “so close so as to basically be the same number”. It is the same number.
They said its the same number though, not basically the same. The idea that as you keep adding 9s to 0.9 you reduce the difference, an infinite amount of 9s yields an infinitely small difference (i.e. no difference) seems sound to me. I think they’re spot on.
No, there is no difference. Infitesimal or otherwise. They are the same number, able to be shown mathematically in a number of ways.
That’s what it means, though. For the function y=x, the limit as x approaches 1, y = 1. This is exactly what the comment of 0.99999… = 1 means. The difference is infinitely small. Infinitely small is zero. The difference is zero.
Infinity small is infinity small. Not zero
That’s simply not true, as I demonstrated in my example.
There is no difference, not even an infinitesimally small one. 1 and 0.999… represent the exact same number.
They only look different because 1/3 out of 1 can’t be represented well in a decimal counting system.
Well, technically “infinitesimally small” means zero sooooooooo
Edit: this is wrong
An infinitesimal is a non-zero number that is closer to zero than any real number. An infinitesimal is what would have to be between 0.999… and 1.
Wait what
I always thought infinitesimal was one of those fake words, like gazillion or something
It sounds like it should be, but it’s actually a real (or, non-real, I suppose, in mathematical terms) thing! :)