infinity
Sign in to savethumb|The Sierpiński triangle contains infinitely many (scaled-down) copies of itself. Infinity is something which is boundless, limitless, endless. It is denoted by , called the infinity symbol.
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Infinity is a concept describing something that is boundless, limitless, and endless—symbolized mathematically by ∞. It matters because it helps us understand patterns and quantities that never stop or repeat indefinitely, like the infinitely many scaled-down copies of itself found in the Sierpiński triangle.
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Article
27 sectionsContents
- History
- Early Greek
- Zeno: Achilles and the tortoise
- Early Indian
- 17th century
- Symbol
- Calculus
- Real analysis
- Complex analysis
- Nonstandard analysis
- Set theory
- Cardinality of the continuum
- Geometry
- Infinite dimension
- Fractals
- Finitism
- Logic
- Applications
- Physics
- Cosmology
- Computing
- Arts, games, and cognitive sciences
- See also
- References
- Bibliography
- Sources
- External links
thumb|The Sierpiński triangle contains infinitely many (scaled-down) copies of itself. Infinity is something which is boundless, limitless, endless. It is denoted by , called the infinity symbol.
From the time of the ancient Greeks, the philosophical nature of infinity has been the subject of debate. In the 17th century, with the introduction of the infinity symbol and infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object.