What is ∞ + ∞ = ????

[Edwardo Piet]

Countable infinite means that you can devise a scheme how to count through the set that will sooner or later reach any arbitrary element of it although.you never finish all of them. You can never finish counting through it because its infinite!

My bold. This is what confuses me. How is it countable if you can never finish counting them? I'm guessing it's a math term as I said, and a technical term as you say, that doesn't literally mean "countable" in the normal dictionary sense of the word.

, but for any element you choose beforehand you can be sure that it will be reached sooner or later. The simplest example is the integers. 0,1,2,3,4... this counting scheme never ends but will eventually reach any number you want even if you can never finish all of them. This is what countable infinite means.

I don't get it. But I don't know math terms like "element" and "integer" so that probably doesn't help.

As opposed to, say, all the real numbers between 0 and 1. There is no way to count through them one by one that ensures that every single one will eventually be reached.

This confuses me so much. I was starting to think maybe it means the real/natural numbers can be counted but not every number including ones with all decimals. But then you say it's opposed to all real numbers.

I don't get it.

I think unless I learn more math then you can keep trying to explain and I still won't get it hehe. Please forgive me if I'm being frustratingly dense.