SUPERINCREASING Meaning and
Definition
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The term "superincreasing" is an adjective used to describe a sequence or set of numbers that exhibits a unique property. In mathematics, a superincreasing sequence is defined as a sequence where each term is greater than the sum of all the preceding terms.
To further clarify this definition, consider a superincreasing sequence {a_1, a_2, a_3, ..., a_n}, where n represents the total number of terms. For this sequence to be superincreasing, it must satisfy the condition a_i > ∑(a_j) for all values of i, where j ranges from 1 to i-1. In simpler terms, each term in the sequence must be larger than the sum of all the preceding terms.
This unique property of superincreasing sequences finds applications in various areas of mathematics and computer science, such as cryptography, algorithm design, and combinatorial optimization. Superincreasing sequences have special properties that make them useful in these fields, and their characteristics can be leveraged to develop efficient algorithms and cryptographic protocols.
In summary, a superincreasing sequence is a sequence of numbers where each term is greater than the sum of all preceding terms. It possesses distinct properties that are valuable in various mathematical and computational applications.
Etymology of SUPERINCREASING
The word "superincreasing" is derived from the combination of two words, "super" and "increasing".
1. "Super": This word comes from the Latin prefix "super-" meaning "above" or "over". It is commonly used to convey the sense of something excessive, superior, or beyond normal limits. In this context, "super" implies that the level of increase being referred to is more than what is typical or expected.
2. "Increasing": This word comes from the Latin word "increas" which means "to grow" or "to augment". It indicates the act or process of getting larger, greater, or more abundant.
By combining these two words, "superincreasing" suggests a level of increase or growth that goes beyond regular or incremental growth, often indicating an exponential or accelerated rate.
