If you are a crossword enthusiast, you might have encountered the clue “Proof finale, in brief” in the New York Times crossword puzzle. The answer is QED, which stands for quod erat demonstrandum, a Latin phrase that means “what was to be demonstrated” or “what was to be shown”. But what does this phrase mean and where does it come from? In this article, we will explore the origin and usage of QED in mathematics, logic, and crossword puzzles.
QED in mathematics and logic
QED is a term that is used to indicate the end of a proof or a logical argument. It signifies that the statement that was to be proven or shown has been successfully derived or deduced from the given premises or axioms. QED is often written or spoken after the last step of a proof or a logical argument to signal its completion and validity.
The origin of QED can be traced back to ancient Greek mathematics, where the phrase ὅπερ ἔδει δεῖξαι (hoper edei deixai) was used to conclude a proof. This phrase means “what was required to be proved” or “what was necessary to be shown”. The Latin translation of this phrase, quod erat demonstrandum, was adopted by medieval and Renaissance scholars who wrote in Latin, and it became a standard notation in mathematical and logical texts.
QED is still used today in formal and informal proofs and arguments, especially in fields such as geometry, logic, and philosophy. It is also sometimes used in other contexts to express a sense of satisfaction, triumph, or finality after making a point or a claim.
QED in crossword puzzles
QED is a common abbreviation that is used in crossword puzzles, especially in the New York Times crossword, which is one of the most popular and prestigious crossword puzzles in the world. QED is often used as a clue for a three-letter word that ends with D, such as “Proof finale, in brief” or “End of a proof, for short”. QED is also sometimes used as an answer for a clue that involves logic, proof, or demonstration, such as “It follows logically” or “Proof of concept”.
QED is a useful word for crossword constructors and solvers, as it is short, easy to remember, and has a high letter value. QED is also a word that can be challenging and rewarding for crossword solvers, as it requires some knowledge of mathematics, logic, and Latin. QED is a word that can enrich the crossword experience and stimulate the mind.
QED is a term that has a long and rich history in mathematics, logic, and crossword puzzles. It is a term that signifies the end of a proof or a logical argument, and it expresses a sense of accomplishment and validity. QED is a term that can also enhance the crossword experience and challenge the crossword solver. QED is a term that is worth knowing and using, whether you are a mathematician, a logician, or a crossword enthusiast. QED.