Infinity (English Wikipedia)

Martin-Löf, Per (1990), "Mathematics of infinity", COLOG-88 (Tallinn, 1988), Lecture Notes in Computer Science, vol. 417, Berlin: Springer, pp. 146–197, doi:10.1007/3-540-52335-9_54, ISBN 978-3-540-52335-2, MR 1064143
Aliprantis, Charalambos D.; Burkinshaw, Owen (1998), Principles of Real Analysis (3rd ed.), San Diego, CA: Academic Press, Inc., p. 29, ISBN 978-0-12-050257-8, MR 1669668, archived from the original on 2015-05-15

ams.org

Schattschneider, Doris (2010). "The Mathematical Side of M. C. Escher" (PDF). Notices of the AMS. 57 (6): 706–718.

archive.org (Global: 6^th place; English: 6^th place)

Hutten, Ernest Hirschlaff (1962). The origins of science; an inquiry into the foundations of Western thought. Internet Archive. London, Allen and Unwin. pp. 1–241. Retrieved 2020-01-09.
Cajori 1993, Sec. 421, Vol. II, p. 44 Cajori, Florian (1993) [1928 & 1929], A History of Mathematical Notations (Two Volumes Bound as One), Dover, ISBN 978-0-486-67766-8
"Arithmetica Infinitorum".
Cajori 1993, Sec. 435, Vol. II, p. 58 Cajori, Florian (1993) [1928 & 1929], A History of Mathematical Notations (Two Volumes Bound as One), Dover, ISBN 978-0-486-67766-8
These uses of infinity for integrals and series can be found in any standard calculus text, such as, Swokowski 1983, pp. 468–510 Swokowski, Earl W. (1983), Calculus with Analytic Geometry (Alternate ed.), Prindle, Weber & Schmidt, ISBN 978-0-87150-341-1
Weeks, Jeffrey (2001). The Shape of Space. CRC Press. ISBN 978-0-8247-0709-5.

arxiv.org (Global: 49^th place; English: 31^st place)

"Infinite Chess, PBS Infinite Series" Archived 2017-04-07 at the Wayback Machine PBS Infinite Series, with academic sources by J. Hamkins (infinite chess: Evans, C.D.A; Joel David Hamkins (2013). "Transfinite game values in infinite chess". arXiv:1302.4377 [math.LO]. and Evans, C.D.A; Joel David Hamkins; Norman Lewis Perlmutter (2015). "A position in infinite chess with game value $ω^4$". arXiv:1510.08155 [math.LO].).

books.google.com (Global: 3^rd place; English: 3^rd place)

Heath, Sir Thomas Little; Heiberg, Johan Ludvig (1908). The Thirteen Books of Euclid's Elements. Vol. v. 1. The University Press. p. 212.
Cauchy, Augustin-Louis (1821). Cours d'Analyse de l'École Royale Polytechnique. Libraires du Roi & de la Bibliothèque du Roi. p. 124. Retrieved October 12, 2019.
Ian Stewart (2017). Infinity: a Very Short Introduction. Oxford University Press. p. 117. ISBN 978-0-19-875523-4. Archived from the original on April 3, 2017.
Cajori, Florian (2007). A History of Mathematical Notations. Vol. 1. Cosimo, Inc. p. 214. ISBN 9781602066854.
Grattan-Guinness, Ivor (2005). Landmark Writings in Western Mathematics 1640-1940. Elsevier. p. 62. ISBN 978-0-08-045744-4. Archived from the original on 2016-06-03. Extract of p. 62
Scott, Joseph Frederick (1981), The mathematical work of John Wallis, D.D., F.R.S., (1616–1703) (2 ed.), American Mathematical Society, p. 24, ISBN 978-0-8284-0314-6, archived from the original on 2016-05-09
O'Flaherty, Wendy Doniger (1986), Dreams, Illusion, and Other Realities, University of Chicago Press, p. 243, ISBN 978-0-226-61855-5, archived from the original on 2016-06-29
Toker, Leona (1989), Nabokov: The Mystery of Literary Structures, Cornell University Press, p. 159, ISBN 978-0-8014-2211-9, archived from the original on 2016-05-09
Aliprantis, Charalambos D.; Burkinshaw, Owen (1998), Principles of Real Analysis (3rd ed.), San Diego, CA: Academic Press, Inc., p. 29, ISBN 978-0-12-050257-8, MR 1669668, archived from the original on 2015-05-15
Rao, Murali; Stetkær, Henrik (1991). Complex Analysis: An Invitation : a Concise Introduction to Complex Function Theory. World Scientific. p. 113. ISBN 9789810203757.
Eric Schechter (2005). Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions (illustrated ed.). Princeton University Press. p. 118. ISBN 978-0-691-12279-3. Extract of page 118
A.W. Moore (2012). The Infinite (2nd, revised ed.). Routledge. p. xiv. ISBN 978-1-134-91213-1. Extract of page xiv
Felix Hausdorff (2021). Set Theory. American Mathematical Soc. p. 44. ISBN 978-1-4704-6494-3. Extract of page 44
Michael Frame; Benoit Mandelbrot (2002). Fractals, Graphics, and Mathematics Education (illustrated ed.). Cambridge University Press. p. 36. ISBN 978-0-88385-169-2. Extract of page 36
Brake, Mark (2013). Alien Life Imagined: Communicating the Science and Culture of Astrobiology (illustrated ed.). Cambridge University Press. p. 63. ISBN 978-0-521-49129-7.
Koupelis, Theo; Kuhn, Karl F. (2007). In Quest of the Universe (illustrated ed.). Jones & Bartlett Learning. p. 553. ISBN 978-0-7637-4387-1. Extract of p. 553
Morris Kline (1985). Mathematics for the Nonmathematician (illustrated, unabridged, reprinted ed.). Courier Corporation. p. 229. ISBN 978-0-486-24823-3. Extract of page 229, Section 10-7

chessvariants.com (Global: low place; English: low place)

Infinite chess at the Chess Variant Pages Archived 2017-04-02 at the Wayback Machine An infinite chess scheme.

compart.com (Global: low place; English: low place)

AG, Compart. "Unicode Character "∞" (U+221E)". Compart.com. Retrieved 2019-11-15.

doi.org (Global: 2^nd place; English: 2^nd place)

Jesseph, Douglas Michael (1998-05-01). "Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes". Perspectives on Science. 6 (1&2): 6–40. doi:10.1162/posc_a_00543. ISSN 1063-6145. OCLC 42413222. S2CID 118227996. Archived from the original on 11 January 2012. Retrieved 1 November 2019 – via Project MUSE.
Goodman, Nicolas D. (1981). "Reflections on Bishop's philosophy of mathematics". In Richman, F. (ed.). Constructive Mathematics. Lecture Notes in Mathematics. Vol. 873. Springer. pp. 135–145. doi:10.1007/BFb0090732. ISBN 978-3-540-10850-4.
Sarton, George (March 1928). "The Thirteen Books of Euclid's Elements. Thomas L. Heath, Heiberg". Isis. 10 (1): 60–62. doi:10.1086/346308. ISSN 0021-1753 – via The University of Chicago Press Journals.
Martin-Löf, Per (1990), "Mathematics of infinity", COLOG-88 (Tallinn, 1988), Lecture Notes in Computer Science, vol. 417, Berlin: Springer, pp. 146–197, doi:10.1007/3-540-52335-9_54, ISBN 978-3-540-52335-2, MR 1064143
Ignacio Jané (May 1995). "The role of the absolute infinite in Cantor's conception of set". Erkenntnis. 42 (3): 375–402. doi:10.1007/BF01129011. JSTOR 20012628. S2CID 122487235. Cantor (1) took the absolute to be a manifestation of God [...] When the absolute is first introduced in Grundlagen, it is linked to God. "the true infinite or absolute, which is in God, admits no kind of determination" (Cantor 1883b, p. 175) This is not an incidental remark, for Cantor is very explicit and insistent about the relation between the absolute and God.
Cohen 1963, p. 1143 Cohen, Paul (1963), "The Independence of the Continuum Hypothesis", Proceedings of the National Academy of Sciences of the United States of America, 50 (6): 1143–1148, Bibcode:1963PNAS...50.1143C, doi:10.1073/pnas.50.6.1143, PMC 221287, PMID 16578557.

doriclenses.com (Global: low place; English: low place)

Doric Lenses Archived 2013-01-24 at the Wayback Machine – Application Note – Axicons – 2. Intensity Distribution. Retrieved 7 April 2014.

free-online.co.uk (Global: low place; English: low place)

rogerstokes.free-online.co.uk

Stokes, Roger (July 2012). "19.2.1". Learning J. Archived from the original on 25 March 2012. Retrieved 6 September 2012.

gnu.org (Global: 1,901^st place; English: 1,743^rd place)

"Infinity and NaN (The GNU C Library)". www.gnu.org. Retrieved 2021-03-15.

hamkins.org (Global: low place; English: low place)

jdh.hamkins.org

Hamkins, Joel David (2012-01-04). "Climb into Cantor's attic". Joel David Hamkins. Retrieved 2026-01-20.

jhu.edu (Global: 560^th place; English: 313^th place)

muse.jhu.edu

Jesseph, Douglas Michael (1998-05-01). "Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes". Perspectives on Science. 6 (1&2): 6–40. doi:10.1162/posc_a_00543. ISSN 1063-6145. OCLC 42413222. S2CID 118227996. Archived from the original on 11 January 2012. Retrieved 1 November 2019 – via Project MUSE.

jstor.org (Global: 23^rd place; English: 15^th place)

Ignacio Jané (May 1995). "The role of the absolute infinite in Cantor's conception of set". Erkenntnis. 42 (3): 375–402. doi:10.1007/BF01129011. JSTOR 20012628. S2CID 122487235. Cantor (1) took the absolute to be a manifestation of God [...] When the absolute is first introduced in Grundlagen, it is linked to God. "the true infinite or absolute, which is in God, admits no kind of determination" (Cantor 1883b, p. 175) This is not an incidental remark, for Cantor is very explicit and insistent about the relation between the absolute and God.

mit.edu (Global: 476^th place; English: 340^th place)

classics.mit.edu

Aristotle. Physics. Translated by Hardie, R. P.; Gaye, R. K. The Internet Classics Archive. Book 3, Chapters 5–8.

nasa.gov (Global: 12^th place; English: 73^rd place)

map.gsfc.nasa.gov

"Will the Universe expand forever?". NASA. 24 January 2014. Archived from the original on 1 June 2012. Retrieved 16 March 2015.

nautil.us (Global: low place; English: low place)

McKee, Maggie (25 September 2014). "Ingenious: Paul J. Steinhardt – The Princeton physicist on what's wrong with inflation theory and his view of the Big Bang". Nautilus. No. 17. NautilusThink Inc. Retrieved 31 March 2017.

nih.gov (Global: 5^th place; English: 5^th place)

ncbi.nlm.nih.gov

Cohen 1963, p. 1143 Cohen, Paul (1963), "The Independence of the Continuum Hypothesis", Proceedings of the National Academy of Sciences of the United States of America, 50 (6): 1143–1148, Bibcode:1963PNAS...50.1143C, doi:10.1073/pnas.50.6.1143, PMC 221287, PMID 16578557.

pubmed.ncbi.nlm.nih.gov

Cohen 1963, p. 1143 Cohen, Paul (1963), "The Independence of the Continuum Hypothesis", Proceedings of the National Academy of Sciences of the United States of America, 50 (6): 1143–1148, Bibcode:1963PNAS...50.1143C, doi:10.1073/pnas.50.6.1143, PMC 221287, PMID 16578557.

oeis.org (Global: 1,188^th place; English: 866^th place)

"List of LaTeX mathematical symbols - OeisWiki". oeis.org. Retrieved 2019-11-15.

oracle.com (Global: 2,532^nd place; English: 1,847^th place)

docs.oracle.com

Gosling, James; et al. (27 July 2012). "4.2.3.". The Java Language Specification (Java SE 7 ed.). California: Oracle America, Inc. Archived from the original on 9 June 2012. Retrieved 6 September 2012.

rit.edu (Global: 8,952^nd place; English: 5,919^th place)

se.rit.edu

Elglaly, Yasmine Nader; Quek, Francis. "Review of "Where Mathematics comes from: How the Embodied Mind Brings Mathematics Into Being" By George Lakoff and Rafael E. Nunez" (PDF). CHI 2009. Archived from the original (PDF) on 2020-02-26. Retrieved 2021-03-25.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Jesseph, Douglas Michael (1998-05-01). "Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes". Perspectives on Science. 6 (1&2): 6–40. doi:10.1162/posc_a_00543. ISSN 1063-6145. OCLC 42413222. S2CID 118227996. Archived from the original on 11 January 2012. Retrieved 1 November 2019 – via Project MUSE.
Ignacio Jané (May 1995). "The role of the absolute infinite in Cantor's conception of set". Erkenntnis. 42 (3): 375–402. doi:10.1007/BF01129011. JSTOR 20012628. S2CID 122487235. Cantor (1) took the absolute to be a manifestation of God [...] When the absolute is first introduced in Grundlagen, it is linked to God. "the true infinite or absolute, which is in God, admits no kind of determination" (Cantor 1883b, p. 175) This is not an incidental remark, for Cantor is very explicit and insistent about the relation between the absolute and God.

stanford.edu (Global: 194^th place; English: 182^nd place)

plato.stanford.edu

"Zeno's Paradoxes". Stanford University. October 15, 2010. Retrieved April 3, 2017.
Bell, John Lane. "Continuity and Infinitesimals". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.

symmetrymagazine.org (Global: low place; English: low place)

"Our universe is Flat". FermiLab/SLAC. 7 April 2015. Archived from the original on 10 April 2015.

tamu.edu (Global: 289^th place; English: 1,073^rd place)

math.tamu.edu

Allen, G Donald (2003). "3 The Emergence of Calculus". The History of Infinity (PDF). Texas A&M University Department of Mathematics. p. 7. Archived from the original (PDF) on August 1, 2020. Retrieved Nov 15, 2019.

uchicago.edu (Global: 226^th place; English: 199^th place)

journals.uchicago.edu

Sarton, George (March 1928). "The Thirteen Books of Euclid's Elements. Thomas L. Heath, Heiberg". Isis. 10 (1): 60–62. doi:10.1086/346308. ISSN 0021-1753 – via The University of Chicago Press Journals.

utexas.edu (Global: 868^th place; English: 634^th place)

farside.ph.utexas.edu

Euclid (2008) [c. 300 BC]. Euclid's Elements of Geometry (PDF). Translated by Fitzpatrick, Richard. Lulu.com. p. 6 (Book I, Postulate 5). ISBN 978-0-6151-7984-1.

web.archive.org (Global: 1^st place; English: 1^st place)

Allen, G Donald (2003). "3 The Emergence of Calculus". The History of Infinity (PDF). Texas A&M University Department of Mathematics. p. 7. Archived from the original (PDF) on August 1, 2020. Retrieved Nov 15, 2019.
Jesseph, Douglas Michael (1998-05-01). "Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes". Perspectives on Science. 6 (1&2): 6–40. doi:10.1162/posc_a_00543. ISSN 1063-6145. OCLC 42413222. S2CID 118227996. Archived from the original on 11 January 2012. Retrieved 1 November 2019 – via Project MUSE.
Ian Stewart (2017). Infinity: a Very Short Introduction. Oxford University Press. p. 117. ISBN 978-0-19-875523-4. Archived from the original on April 3, 2017.
Grattan-Guinness, Ivor (2005). Landmark Writings in Western Mathematics 1640-1940. Elsevier. p. 62. ISBN 978-0-08-045744-4. Archived from the original on 2016-06-03. Extract of p. 62
Scott, Joseph Frederick (1981), The mathematical work of John Wallis, D.D., F.R.S., (1616–1703) (2 ed.), American Mathematical Society, p. 24, ISBN 978-0-8284-0314-6, archived from the original on 2016-05-09
O'Flaherty, Wendy Doniger (1986), Dreams, Illusion, and Other Realities, University of Chicago Press, p. 243, ISBN 978-0-226-61855-5, archived from the original on 2016-06-29
Toker, Leona (1989), Nabokov: The Mystery of Literary Structures, Cornell University Press, p. 159, ISBN 978-0-8014-2211-9, archived from the original on 2016-05-09
Aliprantis, Charalambos D.; Burkinshaw, Owen (1998), Principles of Real Analysis (3rd ed.), San Diego, CA: Academic Press, Inc., p. 29, ISBN 978-0-12-050257-8, MR 1669668, archived from the original on 2015-05-15
Doric Lenses Archived 2013-01-24 at the Wayback Machine – Application Note – Axicons – 2. Intensity Distribution. Retrieved 7 April 2014.
"Will the Universe expand forever?". NASA. 24 January 2014. Archived from the original on 1 June 2012. Retrieved 16 March 2015.
"Our universe is Flat". FermiLab/SLAC. 7 April 2015. Archived from the original on 10 April 2015.
Gosling, James; et al. (27 July 2012). "4.2.3.". The Java Language Specification (Java SE 7 ed.). California: Oracle America, Inc. Archived from the original on 9 June 2012. Retrieved 6 September 2012.
Stokes, Roger (July 2012). "19.2.1". Learning J. Archived from the original on 25 March 2012. Retrieved 6 September 2012.
Infinite chess at the Chess Variant Pages Archived 2017-04-02 at the Wayback Machine An infinite chess scheme.
"Infinite Chess, PBS Infinite Series" Archived 2017-04-07 at the Wayback Machine PBS Infinite Series, with academic sources by J. Hamkins (infinite chess: Evans, C.D.A; Joel David Hamkins (2013). "Transfinite game values in infinite chess". arXiv:1302.4377 [math.LO]. and Evans, C.D.A; Joel David Hamkins; Norman Lewis Perlmutter (2015). "A position in infinite chess with game value $ω^4$". arXiv:1510.08155 [math.LO].).
Elglaly, Yasmine Nader; Quek, Francis. "Review of "Where Mathematics comes from: How the Embodied Mind Brings Mathematics Into Being" By George Lakoff and Rafael E. Nunez" (PDF). CHI 2009. Archived from the original (PDF) on 2020-02-26. Retrieved 2021-03-25.

wikidot.com (Global: 5,548^th place; English: 4,572^nd place)

mathonline.wikidot.com

"Properly Divergent Sequences - Mathonline". mathonline.wikidot.com. Retrieved 2019-11-15.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Jesseph, Douglas Michael (1998-05-01). "Leibniz on the Foundations of the Calculus: The Question of the Reality of Infinitesimal Magnitudes". Perspectives on Science. 6 (1&2): 6–40. doi:10.1162/posc_a_00543. ISSN 1063-6145. OCLC 42413222. S2CID 118227996. Archived from the original on 11 January 2012. Retrieved 1 November 2019 – via Project MUSE.
Gowers, Timothy; Barrow-Green, June (2008). The Princeton companion to mathematics. Imre Leader, Princeton University. Princeton: Princeton University Press. ISBN 978-1-4008-3039-8. OCLC 659590835.
Sarton, George (March 1928). "The Thirteen Books of Euclid's Elements. Thomas L. Heath, Heiberg". Isis. 10 (1): 60–62. doi:10.1086/346308. ISSN 0021-1753 – via The University of Chicago Press Journals.
Russell 1996, p. 347 Russell, Bertrand (1996) [1903], The Principles of Mathematics, New York: Norton, ISBN 978-0-393-31404-5, OCLC 247299160
Bell, John Lane. "Continuity and Infinitesimals". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.

youtube.com (Global: 13^th place; English: 14^th place)

"Infinite Chess, PBS Infinite Series" Archived 2017-04-07 at the Wayback Machine PBS Infinite Series, with academic sources by J. Hamkins (infinite chess: Evans, C.D.A; Joel David Hamkins (2013). "Transfinite game values in infinite chess". arXiv:1302.4377 [math.LO]. and Evans, C.D.A; Joel David Hamkins; Norman Lewis Perlmutter (2015). "A position in infinite chess with game value $ω^4$". arXiv:1510.08155 [math.LO].).

Infinity (English Wikipedia)

acmsonline.org (Global: low place; English: low place)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

ams.org (Global: 434th place; English: 249th place)

mathscinet.ams.org

ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

books.google.com (Global: 3rd place; English: 3rd place)

chessvariants.com (Global: low place; English: low place)

compart.com (Global: low place; English: low place)

doi.org (Global: 2nd place; English: 2nd place)

doriclenses.com (Global: low place; English: low place)

free-online.co.uk (Global: low place; English: low place)

rogerstokes.free-online.co.uk

gnu.org (Global: 1,901st place; English: 1,743rd place)

hamkins.org (Global: low place; English: low place)

jdh.hamkins.org

jhu.edu (Global: 560th place; English: 313th place)

muse.jhu.edu

jstor.org (Global: 23rd place; English: 15th place)

mit.edu (Global: 476th place; English: 340th place)

classics.mit.edu

nasa.gov (Global: 12th place; English: 73rd place)

map.gsfc.nasa.gov

nautil.us (Global: low place; English: low place)

nih.gov (Global: 5th place; English: 5th place)

ncbi.nlm.nih.gov

pubmed.ncbi.nlm.nih.gov

oeis.org (Global: 1,188th place; English: 866th place)

oracle.com (Global: 2,532nd place; English: 1,847th place)

docs.oracle.com

rit.edu (Global: 8,952nd place; English: 5,919th place)

se.rit.edu

semanticscholar.org (Global: 15th place; English: 8th place)

api.semanticscholar.org

stanford.edu (Global: 194th place; English: 182nd place)

plato.stanford.edu

symmetrymagazine.org (Global: low place; English: low place)

tamu.edu (Global: 289th place; English: 1,073rd place)

math.tamu.edu

uchicago.edu (Global: 226th place; English: 199th place)

journals.uchicago.edu

utexas.edu (Global: 868th place; English: 634th place)

farside.ph.utexas.edu

web.archive.org (Global: 1st place; English: 1st place)

wikidot.com (Global: 5,548th place; English: 4,572nd place)

mathonline.wikidot.com

worldcat.org (Global: 4th place; English: 4th place)

search.worldcat.org

youtube.com (Global: 13th place; English: 14th place)

adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ams.org (Global: 434^th place; English: 249^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 49^th place; English: 31^st place)

books.google.com (Global: 3^rd place; English: 3^rd place)

doi.org (Global: 2^nd place; English: 2^nd place)

gnu.org (Global: 1,901^st place; English: 1,743^rd place)

jhu.edu (Global: 560^th place; English: 313^th place)

jstor.org (Global: 23^rd place; English: 15^th place)

mit.edu (Global: 476^th place; English: 340^th place)

nasa.gov (Global: 12^th place; English: 73^rd place)

nih.gov (Global: 5^th place; English: 5^th place)

oeis.org (Global: 1,188^th place; English: 866^th place)

oracle.com (Global: 2,532^nd place; English: 1,847^th place)

rit.edu (Global: 8,952^nd place; English: 5,919^th place)

semanticscholar.org (Global: 15^th place; English: 8^th place)

stanford.edu (Global: 194^th place; English: 182^nd place)

tamu.edu (Global: 289^th place; English: 1,073^rd place)

uchicago.edu (Global: 226^th place; English: 199^th place)

utexas.edu (Global: 868^th place; English: 634^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

wikidot.com (Global: 5,548^th place; English: 4,572^nd place)

worldcat.org (Global: 4^th place; English: 4^th place)

youtube.com (Global: 13^th place; English: 14^th place)