EMPTY SUM Meaning and
Definition
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Empty sum refers to a mathematical term used in algebra and arithmetic where the resulting sum of an operation is defined as having a value of zero. The empty sum is obtained when the set of numbers or elements being added together is empty or when there are no terms involved in the summation. It represents the absence of any element or value in the given set, resulting in a sum of zero.
An empty sum is analogous to an empty container, which holds no objects or has no contents. It is a special case where no numerical value is present, and thus, the sum is considered empty. This concept is particularly significant in mathematical proofs and theories, as it helps to establish foundational principles and solve complex problems.
The empty sum has unique properties when it comes to mathematical operations. For example, adding zero to any number or adding any number to zero does not change the value of that number. Hence, the empty sum serves as the neutral element or identity element- a value that when combined with any other value, does not change it.
In summary, an empty sum refers to the sum of a set or series of numbers with no elements or terms, resulting in a sum of zero. It is a fundamental concept in mathematics that plays a crucial role in algebraic operations and acts as the identity element for addition.
Etymology of EMPTY SUM
The term "empty sum" is derived from the combination of the words "empty" and "sum".
- The word "empty" comes from the Middle English word "emty", which evolved from the Old English word "ǣmetta", meaning "lacking, vacant, or unoccupied". The word "empty" refers to something that contains nothing or has nothing inside it.
- The word "sum" comes from the Latin word "summa", which means "the highest part or whole" or "the total". It refers to the result obtained by adding numbers or quantities together.
When these two words are combined, "empty sum" refers to the total or sum of nothing, which implies that there is no value or amount involved. In mathematics, it is often used to describe the result of adding zero to any number, resulting in the original number.
