..." signifies that at least one such member exists, though you haven't identified exactly which one yet.
: Use this when introducing something new to the conversation. In mathematical logic, "There exists a number Exists
In standard English, is a verb, not a noun, so it does not take an article itself . However, the choice of article for the noun following it (e.g., "There exists a ..." vs. "There exists the ...") depends on whether the object is being introduced for the first time or is already known. Indefinite vs. Definite Articles is a verb