Finiteness, finitude, or being finite, is the state of being limited or having an end, and is a counter to the concept of infinity. Humans are considered to be in this state because of their limited life span, uniformly ending in death. Each natural number is considered to be in this state, because counting up to that number stops when the number is reached. The concept appears across disciplines, from mathematics and linguistics to philosophy, where it is used to describe quantities, structures, and conditions. In mathematics, a set or number is finite if it is limited in size, while in linguistics, a verb is finite if it is limited by grammatical features such as tense, person, and number, which definition allows it to stand alone as the main verb of a clause. Philosophers including Georg Wilhelm Friedrich Hegel, Martin Heidegger, and Jacques Derrida have explored finiteness as a fundamental feature of human existence, emphasizing how boundaries, endings, and mortality shape meaning and understanding.
👉 Finiteness in the context of Sequential
In mathematics, a sequence is a collection of objects possibly with repetition, that come in a specified order. Like a set, it contains members (also called elements, or terms). Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.
For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of even positive integers (2, 4, 6, ...), meaning that each element is twice the value of its position.
Finiteness in the context of Finite set
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example,
is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the cardinality (or the cardinal number) of the set. A set that is not a finite set is called an infinite set. For example, the set of all positive integers is infinite:
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