The spelling of the phrase "are even" is a simple combination of two common words in the English language. The word "are" is spelled with the phonetic transcription /ɑr/ and is commonly used to indicate the present tense of the verb "to be". The word "even", on the other hand, is spelled with the phonetic transcription /ˈivən/ and is used to describe something that is equal or balanced. Together, "are even" can mean that something is equal or balanced in the present tense.
"Are even" is a term used to describe a situation where a set of numbers or objects can be divided or grouped equally into pairs without any remainder. In mathematics, "even" refers to an integer that is divisible by 2 without leaving a remainder. When discussing numbers, the phrase "are even" indicates that the numbers being referred to satisfy this condition.
To elaborate, if a set of numbers "are even", it means that each number in the set can be divided by 2 to give an integer result. For example, the set {4, 8, 12, 16} are even numbers because they can all be divided by 2 to obtain whole numbers (2, 4, 6, and 8 respectively).
In a broader sense, "are even" can also be used in other contexts to describe situations where there is an equal distribution, balance, or symmetry. In this usage, "are even" implies that the elements being referred to are divided or distributed evenly among groups or individuals, without any excess or inequality.
Overall, "are even" primarily revolves around the concept of divisibility by 2 in numerical contexts, while also carrying connotations of balance and symmetry in broader contexts.
The phrase "are even" doesn't have a separate etymology itself, as it is a combination of two separate words: "are" and "even".
1. "Are" is the present plural form of the verb "to be", which comes from Old English "eart" (2nd person singular) and "sind" (3rd person plural). These Old English forms can be traced back to the Proto-Germanic root "esar" meaning "to be". The same root can be seen in related Germanic languages like German ("sind") and Dutch ("zijn").
2. "Even" comes from Middle English "even", which was derived from Old English "efne" meaning "level" or "equal". This Old English term can be traced further back to the Proto-Germanic root *ebniz.