Tattoo Pics of Infinity, Infinity Sign and Family

Mathematical symbol, "∞"

${\displaystyle \infty }$
Infinity symbol
In Unicode	U+221E ∞ INFINITY (HTML∞· ∞)
Dissimilar from
Different from	U+267E ♾ PERMANENT PAPER SIGN (HTML♾)

The infinity symbol ( ${\displaystyle \infty }$ ) is a mathematical symbol representing the concept of infinity. This symbol is also chosen a lemniscate,^[ane] after the lemniscate curves of a like shape studied in algebraic geometry,^[ii] or "lazy 8", in the terminology of livestock branding.^[three]

This symbol was first used mathematically by John Wallis in the 17th century, although it has a longer history of other uses. In mathematics, it oft refers to infinite processes (potential infinity) rather than infinite values (bodily infinity). It has other related technical meanings, such as the use of long-lasting paper in bookbinding, and has been used for its symbolic value of the space in modern mysticism and literature. It is a common element of graphic design, for example in corporate logos as well as in older designs such as the Métis flag.

Both the infinity symbol itself and several variations of the symbol are bachelor in various character encodings.

History [edit]

John Wallis introduced the infinity symbol ${\displaystyle \infty }$ to mathematical literature.

The ${\displaystyle \infty }$ symbol in several typefaces

The lemniscate has been a common decorative motif since ancient times; for instance it is commonly seen on Viking Age combs.^[iv]

The English mathematician John Wallis is credited with introducing the infinity symbol with its mathematical pregnant in 1655, in his De sectionibus conicis.^{[5] [6] [7]} Wallis did not explain his choice of this symbol. It has been conjectured to be a variant grade of a Roman numeral, but which Roman numeral is unclear. One theory proposes that the infinity symbol was based on the numeral for 100 meg, which resembled the same symbol enclosed within a rectangular frame.^[8] Another proposes instead that information technology was based on the annotation CIↃ used to represent 1,000.^[9] Instead of a Roman numeral, it may alternatively exist derived from a variant of ω, the lower-example grade of omega, the last letter in the Greek alphabet.^[nine]

Perchance in some cases because of typographic limitations, other symbols resembling the infinity sign have been used for the same meaning.^[7] Leonhard Euler used an open letterform more closely resembling a reflected and sideways South than a lemniscate,^[10] and fifty-fifty "O–O" has been used as a stand up-in for the infinity symbol itself.^[vii]

Usage [edit]

Mathematics [edit]

In mathematics, the infinity symbol is used more oftentimes to correspond a potential infinity,^[11] rather than an actually infinite quantity as included in the extended real numbers, the cardinal numbers and the ordinal numbers (which employ other notations, such equally ${\displaystyle \,\aleph _{0}\,}$ and ω, for infinite values). For instance, in mathematical expressions with summations and limits such every bit

$${\displaystyle \sum _{n=0}^{\infty }{\frac {one}{two^{n}}}=\lim _{x\to \infty }{\frac {2^{x}-i}{2^{ten-1}}}=two,}$$

the infinity sign is conventionally interpreted as pregnant that the variable grows arbitrarily large towards infinity, rather than actually taking an space value, although other interpretations are possible.^[12]

The infinity symbol may also be used to represent a betoken at infinity, especially when there is only one such indicate under consideration. This usage includes, in particular, the infinite bespeak of a projective line,^[13] and the signal added to a topological space to form its one-point compactification.^[fourteen]

Other technical uses [edit]

Side view of a camera lens, showing infinity symbol on the focal length indicator

In areas other than mathematics, the infinity symbol may take on other related meanings. For instance, it has been used in bookbinding to indicate that a book is printed on acid-gratuitous paper and will therefore be long-lasting.^[15] On cameras and their lenses, the infinity symbol indicates that the lens's focal length is set to an infinite altitude, and is "probably one of the oldest symbols to exist used on cameras".^[16]

Symbolism and literary uses [edit]

In modern mysticism, the infinity symbol has become identified with a variation of the ouroboros, an ancient image of a snake eating its ain tail that has also come to symbolize the infinite, and the ouroboros is sometimes drawn in figure-eight grade to reflect this identification—rather than in its more than traditional circular form.^[18]

In the works of Vladimir Nabokov, including The Gift and Stake Fire, the figure-eight shape is used symbolically to refer to the Möbius strip and the infinite, as is the example in these books' descriptions of the shapes of cycle tire tracks and of the outlines of half-remembered people. Nabokov's poem after which he entitled Stake Fire explicitly refers to "the miracle of the lemniscate".^[xix] Other authors whose works use this shape with its symbolic pregnant of the space include James Joyce, in Ulysses,^[xx] and David Foster Wallace, in Infinite Jest.^[21]

Graphic design [edit]

The well-known shape and meaning of the infinity symbol accept fabricated it a common typographic element of graphic design. For instance, the Métis flag, used by the Canadian Métis people since the early on 19th century, is based around this symbol.^[22] Different theories accept been put forrad for the meaning of the symbol on this flag, including the hope for an space futurity for Métis culture and its mix of European and Beginning Nations traditions,^{[23] [24]} but also evoking the geometric shapes of Métic dances,^[25], Celtic knots,^[26] or Plains Outset Nations Sign Language.^[27]

A rainbow-coloured infinity symbol is also used by the neurodiversity movement, as a fashion to symbolize the infinite variation of the people in the movement and of human cognition.^[28] The Bakelite company took up this symbol in its corporate logo to refer to the broad range of varied applications of the constructed cloth they produced.^[29] Versions of this symbol have been used in other trademarks, corporate logos, and emblems including those of Fujitsu,^[thirty] Cell Printing,^[31] and the 2022 FIFA World Cup.^[32]

Encoding [edit]

The symbol is encoded in Unicode at U+221E ∞ INFINITY ^[33] and in LaTeX as \infty: ${\displaystyle \infty }$ .^[34] An encircled version is encoded for use as a symbol for acid-free newspaper.

Graphic symbol information

Preview	∞		♾
Unicode name	INFINITY		PERMANENT PAPER SIGN
Encodings	decimal	hex	december	hex
Unicode	8734	U+221E	9854	U+267E
UTF-8	226 136 158	E2 88 9E	226 153 190	E2 99 Exist
GB 18030	161 222	A1 DE	129 55 174 56	81 37 AE 38
Numeric character reference	∞	∞	♾	♾
Named grapheme reference	∞
OEM-437 (Alt Code)[35]	236	EC
Mac Bone Roman[36]	176	B0
Symbol Font encoding[37]	165	A5
Shift JIS[38]	129 135	81 87
EUC-JP[39]	161 231	A1 E7
EUC-KR[40] / UHC[41]	161 196	A1 C4
EUC-KPS-9566[42]	162 172	A2 Air-conditioning
Big5[43]	161 219	A1 DB
LaTeX[34]	\infty		\acidfree
CLDR text-to-spoken communication name[44]			infinity

The Unicode prepare of symbols also includes several variant forms of the infinity symbol that are less oftentimes bachelor in fonts in the block Miscellaneous Mathematical Symbols-B.^[45]

Character information

Preview	⧜		⧝		⧞
Unicode name	INCOMPLETE INFINITY		Necktie OVER INFINITY		INFINITY NEGATED WITH VERTICAL BAR
Encodings	decimal	hex	dec	hex	dec	hex
Unicode	10716	U+29DC	10717	U+29DD	10718	U+29DE
UTF-viii	226 167 156	E2 A7 9C	226 167 157	E2 A7 9D	226 167 158	E2 A7 9E
Numeric character reference	⧜	⧜	⧝	⧝	⧞	⧞
Named character reference	⧜		⧝		⧞
LaTeX[34]	\iinfin		\tieinfty		\nvinfty

Come across also [edit]

• Aleph number
• History of mathematical note
• Lazy 8 (disambiguation)

References [edit]

1. ^ Rucker, Rudy (1982). Infinity and the Listen: The scientific discipline and philosophy of the infinite. Boston, Massachusetts: Birkhäuser. p. 1. ISBN3-7643-3034-1. MR 0658492.
2. ^ Erickson, Martin J. (2011). "one.one Lemniscate". Beautiful Mathematics. MAA Spectrum. Mathematical Association of America. pp. 1–three. ISBN978-0-88385-576-8.
3. ^ Humez, Alexander; Humez, Nicholas D.; Maguire, Joseph (1993). Zero to Lazy Eight: The Romance of Numbers. Simon and Schuster. p. 18. ISBN978-0-671-74281-2.
4. ^ van Riel, Sjoerd (2017). "Viking Age Combs: Local Products or Objects of Merchandise?". Lund Archaeological Review. 23: 163–178. Meet p. 172: "Within this type the lemniscate (∞) is a commonly used motif."
5. ^ Wallis, John (1655). "Pars Prima". De Sectionibus Conicis, Nova Methodo Expositis, Tractatus (in Latin). pp. 4.
6. ^ Scott, Joseph Frederick (1981). The mathematical piece of work of John Wallis, D.D., F.R.S., (1616-1703) (2nd ed.). American Mathematical Guild. p. 24. ISBN0-8284-0314-7.
7. ^ ^{a b c} Cajori, Florian (1929). "Signs for infinity and transfinite numbers". A History of Mathematical Notations, Book II: Notations Mainly in College Mathematics. Open Court. pp. 44–48.
8. ^ Maor, Eli (1991). To Infinity and Across: A Cultural History of the Space. Princeton, New Jersey: Princeton University Press. p. 7. ISBN0-691-02511-viii. MR 1129467.
9. ^ ^{a b} Clegg, Brian (2003). "Chapter 6: Labelling the space". A Brief History of Infinity: The Quest to Think the Unthinkable. Constable & Robinson Ltd. ISBN978-1-84119-650-3.
10. ^ Cajori (1929) displays this symbol incorrectly, equally a turned S without reflection. It can be seen as Euler used it on page 174 of Euler, Leonhard (1744). "Variae observationes circa serial infinitas" (PDF). Commentarii academiae scientiarum Petropolitanae (in Latin). 9: 160–188.
11. ^ Barrow, John D. (2008). "Infinity: Where God Divides by Zero". Cosmic Imagery: Key Images in the History of Science. W. W. Norton & Company. pp. 339–340. ISBN978-0-393-06177-2.
12. ^ Shipman, Barbara A. (April 2013). "Convergence and the Cauchy property of sequences in the setting of bodily infinity". PRIMUS. 23 (5): 441–458. doi:ten.1080/10511970.2012.753963.
13. ^ Perrin, Daniel (2007). Algebraic Geometry: An Introduction. Springer. p. 28. ISBN978-one-84800-056-8.
14. ^ Aliprantis, Charalambos D.; Edge, Kim C. (2006). Infinite Dimensional Analysis: A Hitchhiker'due south Guide (3rd ed.). Springer. pp. 56–57. ISBN978-three-540-29587-7.
15. ^ Zboray, Ronald J.; Zboray, Mary Saracino (2000). A Handbook for the Study of Volume History in the United States. Middle for the Book, Library of Congress. p. 49. ISBN978-0-8444-1015-ix.
16. ^ Crist, Brian; Aurello, David North. (October 1990). "Development of camera symbols for consumers". Proceedings of the Human Factors Society Almanac Coming together. 34 (5): 489–493. doi:ten.1177/154193129003400512.
17. ^ Armson, Morandir (June 2011). "The transitory tarot: an examination of tarot cards, the 21st century New Historic period and theosophical thought". Literature & Aesthetics. 21 (i): 196–212. See in particular p. 203: "Reincarnation is symbolised in a number of cards within the Waite-Smith tarot deck. The primary symbols of reincarnation used are the infinity symbol or lemniscate, the bicycle and the circumvolve."
18. ^ O'Flaherty, Wendy Doniger (1986). Dreams, Illusion, and Other Realities. Academy of Chicago Printing. p. 243. ISBN978-0-226-61855-v. The book likewise features this image on its cover.
19. ^ Toker, Leona (1989). Nabokov: The Mystery of Literary Structures . Cornell Academy Press. p. 159. ISBN978-0-8014-2211-9.
20. ^ Bahun, Sanja (2012). "'These heavy sands are linguistic communication tide and wind accept silted here': Tidal voicing and the poetics of home in James Joyce's Ulysses". In Kim, Rina; Westall, Claire (eds.). Cross-Gendered Literary Voices: Appropriating, Resisting, Embracing. Palgrave Macmillan. pp. 57–73. doi:10.1057/9781137020758_4.
21. ^ Natalini, Roberto (2013). "David Foster Wallace and the mathematics of infinity". In Boswell, Marshall; Fire, Stephen J. (eds.). A Companion to David Foster Wallace Studies. American Literature Readings in the 21st Century. Palgrave Macmillan. pp. 43–57. doi:x.1057/9781137078346_3.
22. ^ Healy, Donald T.; Orenski, Peter J. (2003). Native American Flags. University of Oklahoma Printing. p. 284. ISBN978-0-8061-3556-4.
23. ^ Gaudry, Adam (Spring 2018). "Communing with the Dead: The "New Métis," Métis Identity Appropriation, and the Displacement of Living Métis Culture". American Indian Quarterly. 42 (2): 162–190. doi:x.5250/amerindiquar.42.2.0162. JSTOR 10.5250/amerindiquar.42.2.0162. S2CID 165232342.
24. ^ "The Métis flag". Gabriel Dumont Institute(Métis Culture & Heritage Resources Centre). Archived from the original on 2013-07-24.
25. ^ Racette, Calvin (1987). Flags of the Métis (PDF). Gabriel Dumont Found. ISBN0-920915-18-iii.
26. ^ Darren R., Préfontaine (2007). "Flight the Flag, Editor'due south note". New Brood Magazine (Wintertime 2007): 6. Retrieved 2020-08-26 .
27. ^ Barkwell, Lawrence J. "The Metis Infinity Flag". Virtual Museum of Métis History and Culture. Gabriel Dumont Institute. Retrieved 2020-07-15 .
28. ^ Gross, Liza (September 2016). "In search of autism'due south roots". PLOS Biology. 14 (9): e2000958. doi:10.1371/periodical.pbio.2000958.
29. ^ Crespy, Daniel; Bozonnet, Marianne; Meier, Martin (April 2008). "100 years of Bakelite, the material of a m uses". Angewandte Chemie. 47 (xviii): 3322–3328. doi:10.1002/anie.200704281.
30. ^ Rivkin, Steve; Sutherland, Fraser (2005). The Making of a Name: The Inside Story of the Brands We Buy. Oxford University Press. p. 130. ISBN978-0-19-988340-0.
31. ^ Willmes, Claudia Gisela (January 2021). "Scientific discipline that inspires". Trends in Molecular Medicine. 27 (1): 1. doi:x.1016/j.molmed.2020.xi.001. PMID 33308981.
32. ^ "Qatar 2022: Football World Cup logo unveiled". Al Jazeera. September 3, 2019.
33. ^ "Unicode Character "∞" (U+221E)". Unicode. Compart AG. Retrieved 2019-11-15 .
34. ^ ^{a b c} Pakin, Scott (May 5, 2021). "Tabular array 294: stix Infinities". The Comprehensive LATEX Symbol List. CTAN. p. 118. Retrieved 2022-02-19 .
35. ^ Steele, Shawn (April 24, 1996). "cp437_DOSLatinUS to Unicode table". Unicode Consortium. Retrieved 2022-02-19 .
36. ^ "Map (external version) from Mac Bone Roman character set to Unicode two.1 and afterwards". Apple Inc. April 5, 2005. Retrieved 2022-02-nineteen – via Unicode Consortium.
37. ^ "Map (external version) from Mac OS Symbol character set to Unicode 4.0 and later". Apple Inc. April 5, 2005. Retrieved 2022-02-19 – via Unicode Consortium.
38. ^ "Shift-JIS to Unicode". Unicode Consortium. December ii, 2015. Retrieved 2022-02-19 .
39. ^ "EUC-JP-2007". International Components for Unicode. Unicode Consortium. Retrieved 2022-02-19 – via GitHub.
40. ^ "IBM-970". International Components for Unicode. Unicode Consortium. May nine, 2007. Retrieved 2022-02-nineteen – via GitHub.
41. ^ Steele, Shawn (January vii, 2000). "cp949 to Unicode table". Unicode Consortium. Retrieved 2022-02-nineteen .
42. ^ "KPS 9566-2003 to Unicode". Unicode Consortium. Apr 27, 2011. Retrieved 2022-02-19 .
43. ^ van Kesteren, Anne. "big5". Encoding Standard. WHATWG.
44. ^ Unicode, Inc. "Annotations". Mutual Locale Data Repository – via GitHub.
45. ^ "Miscellaneous Mathematical Symbols-B" (PDF). Unicode Consortium. Archived (PDF) from the original on 2018-11-12. Retrieved 2022-02-19 .

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Source: https://en.wikipedia.org/wiki/Infinity_symbol

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