végtelendimenziós

Végtelendimenziós is a Hungarian term that translates to "infinite-dimensional" in English. It is most commonly encountered in the context of mathematics, particularly in functional analysis and linear algebra.

In mathematics, a vector space is considered infinite-dimensional if it cannot be spanned by a finite number of vectors. This means that any finite set of vectors within the space will not be sufficient to form every other vector in the space through linear combinations. Examples of infinite-dimensional spaces include the space of all continuous functions on a given interval, or the space of all square-summable sequences. These spaces are fundamental to understanding many advanced mathematical concepts and have applications in areas such as quantum mechanics and signal processing.

The concept of infinite-dimensionality is crucial for extending concepts from finite-dimensional vector spaces, like basis and dimension, to more complex mathematical structures. While intuitive notions of dimension, such as geometric dimensions (0D point, 1D line, 2D plane, 3D space), are based on finite counts, infinite-dimensional spaces require more abstract definitions and tools for analysis. The study of such spaces forms a significant part of modern mathematics.