computable numbers

Computable numbers are real numbers for which there exists a precise, systematic method—called an algorithm—that can generate their decimal expansion to any desired degree of accuracy. In other words, given enough time and the right procedure, you can compute their digits step-by-step. These numbers encompass many familiar constants like π and e, but exclude some real numbers that cannot be exactly calculated by any algorithm. Computable numbers bridge mathematics and computer science, illustrating the limits of what machines can precisely determine within the infinite landscape of real numbers.