In any particular textbook or paper, the way in which these symbols should be interpreted should generally be clear from the context and definitions. (The upper-case letters in gray are not used as Greek symbols per se, because they are generally indistinguishable from their Roman-letter equivalents.) The lower-case letters are most often used for variables, such as angles and complex numbers, and for functions and formulas, while the upper-case letters more commonly stand for sets and spaces, and sometimes for repeated arithmetic operations such as adding and multiplying (see Sigma and Pi). The lower-case letters are used more often than the upper-case letters, but the latter are used often enough. The table below lists all of the letters in the Greek alphabet, upper-case and lower-case, with their names and pronunciations. Since then, each new generation of mathematicians has just gotten used to using them. However, at the time they were introduced most scholars had been taught at least some Latin and Greek during their education, so the letters did not seem nearly so strange to them as they do to us. To us these symbols may seem quite foreign, and they are difficult to become familiar with. Mathematics requires a large number of symbols to stand for abstract objects, such as numbers, sets, functions, and spaces, so the use of Greek letters was introduced long ago to provide a collection of useful symbols to supplement the usual Roman letters. Zeno’s Paradox of the Tortoise and Achilles.