Comment on I just cited myself.

<- View Parent
sp3tr4l@lemmy.zip ⁨4⁩ ⁨months⁩ ago

The ellipsis notation generally refers to repetition of a pattern.

Ok. In mathematical notation/context, it is more specific, as I outlined.

0.999… is a real number, and not any object that can be said to converge. It is exactly 1.

Ok. Never said 0.999… is not a real number. Yep, it is exactly 1 because solving the equation it truly represents, a geometric series, results in 1. This solution is obtained using what is called the convergence theorem or rule, as I outlined.

In what way is it distinct?

0.424242… solved via the convergence theorem simply results in itself, as represented in mathematical nomenclature.

0.999… does not again result in 0.999…, but results to 1, a notably different representation that causes the entire discussion in this thread.

And what is a ‘repeating number’? Did you mean ‘repeating decimal’?

I meant what I said: “know patterns of repeating numbers after the decimal point.”

Perhaps I should have also clarified known finite patterns to further emphasize the difference between rational and irrational numbers.

source
Sort:hotnewtop