[ajkjk]

What are you talking about? Infinite decimals give reals, do they not? Repeating decimals give rational which are a subset of the reals.

The colloquial phrase 'infinite decimal' is perfectly intelligible without reference to whether it's an infinite amount of data or rigorously defined or whatever else.

There's a lot of trickery involved din dealing with the reals formally but they're still easy to conceptualize intuitively.

[nilkn]

“What I’m taking about” is that they are not easy to conceptualize intuitively.

If I were a skeptic of real numbers, I’d tell you that talking about an infinite decimal expansion that never terminated and contains no repeating pattern is nonsense. I’d say such a thing doesn’t exist, because you can’t specify a single example by writing down its decimal expansion — by definition. So if that’s the only idea you have to convince a skeptic, you’ve already failed and are out of the game. To convince the skeptic, you’d have to develop a more sophisticated method to show indirectly an example of a real number that is not rational (for instance, perhaps by proving that, should sqrt(2) exist, it cannot be rational).

[ajkjk]

I guess we are talking about different things. It seems to me that it's trivial to imagine then conceptually. They go on forever and most of them never repeat? Sounds good to me. Sqrt(2) never repeats? sure, whatever. I never found the proofs of this stuff very interesting.

Now, I am a skeptic of their use in physics / science. But that's a different question, and more about pedagogy than the raw content of the theories.