original passage: A real number "a" is first-order definable in the language of set theory, without parameters, if there is a formula "φ" in the language of set theory, with one free variable, such that "a" is the unique real number such that "φ"("a") holds (see). This notion cannot be expressed as a formula in the language of set theory.
original sentence: This notion cannot be expressed as a formula in the language of set theory.
sentence2: Would a gifted student from a science, technology, or engineering field, who had studied enough math to handle all practical applications yet had mostly avoided more theoretical aspects such as set theory, be able to express this notion as a formula, if asked, even if the result had little to no meaning to said student?
sentence1: A real number "a" is first-order definable in the language of set theory, without parameters, if there is a formula "φ" in the language of set theory, with one free variable, such that "a" is the unique real number such that "φ"("a") holds (see). Using the language of set theory, it is impossible to express this notion as a formula.