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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
by Eddy_Viscosity2 1y ago
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.
- drdeca 1y agoThe decimal places are just a way of representing it.
- Eddy_Viscosity2 1y agoThe 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.
- drdeca 1y agoNo, 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.
- drdeca 1y agoDang autocorrect. “sideline” should be Dedekind
- empath75 1y agoYou absolutely cannot visualize the concept "2" in your head. You can only visualize "two things" or the word "two" or the symbol "2", but the actual concept "2" is just as abstract as a real number. You might say, I can imagine 2 apples, but I can't imagine pi apples, but you could just as easily imagine unrolling a circle with a diameter of 1, and you have visualized "pi" just as well as you can visualize 2 apples.