You can hold a two in your head, but you can't hold a number with infinitely many decimal places. Any manipulations you do with the real 2 are done conceptually whereas with the natural 2, its done concretely.
You can hold a two in your head, but you can't hold a number with infinitely many decimal places. Any manipulations you do with the real 2 are done conceptually whereas with the natural 2, its done concretely.
The decimal places are just a way of representing it.
The infinite number of decimal places is the definitional feature of a real number. No matter how's it represented they are still there and cannot be contained in our brains. We can say pi and hold the concept of pi in our heads, but not the actual number.
No, it really isn’t. The real numbers can be constructed in a number of ways, and it is more common to define them as either Dedekind cuts, or equivalence classes of Cauchy sequences of rational numbers.
Personally, I’d go with the sideline cut definition.
Dang autocorrect. “sideline” should be Dedekind