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{{short description|Cloud-based LaTeX editor}}
{{Infobox software
| title = Overleaf
| screenshot = Screenshot of Overleaf.png
| logo = Overleaf Logo.svg
| logo size = 86
| screenshot size = 270
| caption = Overleaf running as a [[Progressive web app|PWA]] on [[Windows 11]]
| author = John Hammersley and John Lees-Miller
| repo = https://github.com/overleaf/
| genre = [[Web application]]
| license = [[AGPLv3]]
| website = https://www.overleaf.com/
}}


\textbf{Claim:} The set of positive integers that contains the integer 1 and has the property that if it contains all the positive integers 1, 2, ..., k, then it also contains the integer k+1, must be the set of all positive integers.
'''Overleaf''' is a collaborative cloud-based [[LaTeX]] editor used for writing, editing and publishing scientific documents.<ref name="SimplyStatistics" /><ref name="OverleafAbout" />

\textbf{Proof by Principle of Mathematical Induction (PMI):}
It partners with a wide range of scientific publishers to provide official journal LaTeX templates, and direct submission links.<ref name="ScholarOne" /><ref name="AIP" /><ref name="OverleafDirectSubmissionLink" />

\textbf{Step 1: Base Case:} Let k = 1. In this case, the set contains only the integer 1, and it trivially contains the integer 2 (k+1 = 1+1 = 2). Therefore, the property holds for the base case.
Overleaf was conceived by John Hammersley and John Lees-Miller, who started developing it in 2011<ref name="JEP" /> as WriteLaTeX, through their company WriteLaTeX Limited.<ref name="CompaniesHouseGovUK" /><ref name="OpenGovUK" /><ref name="Endole" /><ref name="DueDil" /><ref name="StartupBeat" /> Both are mathematicians and were inspired by their own experiences in academia to create a better solution for collaborative scientific writing.<ref name="OnYourWavelength" /><ref name="DigitalScience" /> They launched a beta version of Overleaf on 16 January 2014, at the first #FuturePub event, held at the British Library in London.<ref name="Freyfogle" /><ref name="ScholCommsProd" />

\textbf{Step 2: Inductive Hypothesis:} Assume that the property holds for some positive integer n, where n ≥ 1. That is, if the set contains all the positive integers 1, 2, ..., n, then it also contains the integer n+1.
After merging with ShareLaTeX in 2017, they released Overleaf v2, combining original features from both into a single cloud-based platform.<ref name="ShareLaTeX.com" />
\textbf{Step 3: Inductive Step:} We need to prove that the property holds for n+1. That is, if the set contains all the positive integers 1, 2, ..., n+1, then it also contains the integer (n+1)+1 = n+2.
By the inductive hypothesis, we know that the set containing all the positive integers 1, 2, ..., n also contains the integer n+1. Now, if we add the integer n+2 to this set, it will still contain all the positive integers 1, 2, ..., n+1. Therefore, the property holds for n+1.
By the principle of mathematical induction, we have shown that if the set contains the integer 1 and if it contains all the positive integers 1, 2, ..., k, then it also contains the integer k+1, for all positive integers k. Therefore, the set of positive integers satisfying this property is the set of all positive integers.
\qed


== History ==
== History ==

Revision as of 08:30, 3 March 2024

\textbf{Claim:} The set of positive integers that contains the integer 1 and has the property that if it contains all the positive integers 1, 2, ..., k, then it also contains the integer k+1, must be the set of all positive integers.

\textbf{Proof by Principle of Mathematical Induction (PMI):}

\textbf{Step 1: Base Case:} Let k = 1. In this case, the set contains only the integer 1, and it trivially contains the integer 2 (k+1 = 1+1 = 2). Therefore, the property holds for the base case.

\textbf{Step 2: Inductive Hypothesis:} Assume that the property holds for some positive integer n, where n ≥ 1. That is, if the set contains all the positive integers 1, 2, ..., n, then it also contains the integer n+1.

\textbf{Step 3: Inductive Step:} We need to prove that the property holds for n+1. That is, if the set contains all the positive integers 1, 2, ..., n+1, then it also contains the integer (n+1)+1 = n+2.

By the inductive hypothesis, we know that the set containing all the positive integers 1, 2, ..., n also contains the integer n+1. Now, if we add the integer n+2 to this set, it will still contain all the positive integers 1, 2, ..., n+1. Therefore, the property holds for n+1.

By the principle of mathematical induction, we have shown that if the set contains the integer 1 and if it contains all the positive integers 1, 2, ..., k, then it also contains the integer k+1, for all positive integers k. Therefore, the set of positive integers satisfying this property is the set of all positive integers.

\qed

History

Overleaf was selected as one of the ten teams who participated to the 2013 Summer's Bethnal Green Ventures (BGV) accelerator programme.[1][2][3] That program started on the July 1, 2013, and lasted for 3 months.[4][5][6] The Demo Day of that BGV 2013 Summer program was held on the September 19, 2013.[7]

The company received strategic investment from Digital Science in 2014.[8][9][10][11] Overleaf won Innovative Internet Business at the 2014 Nominet Internet Awards,[12] and featured 99th in SyndicateRoom's 2018 list of Britain's top 100 fastest-growing business.[13]

Overleaf has been discussed as a tool for writing scientific publications in Nature,[14] Science,[15] Red Hat's opensource.com[16] and the German IT magazine Heise Online.[17] "In 2017, CERN, Europe’s particle-physics laboratory near Geneva, Switzerland, adopted Overleaf as its preferred collaborative authoring platform."[14][18]

Overleaf provides templates for submission to scientific journals and conferences. For example, the IEEE[19] and Springer[20] (incl. Nature[21]) mention the possibility for submission using Overleaf.

Merge with ShareLaTeX

On 20 July 2017, Overleaf acquired ShareLaTeX to create a combined community of over two million users.[22][23][24] This led to the creation of Overleaf v2, combining original features from both into a single cloud-based platform hosted at overleaf.com.[24]

In May 2021, Lees-Miller (Overleaf), Paulo Reis (Overleaf), and Sven Laqua (Digital Science) were awarded the SIGCHI Best Case Study Award at the ACM CHI2021 Conference for their case study "Merging SaaS Products In A User-Centered Way: A Case Study of Overleaf and ShareLaTeX”.[25][26]

See also

References

  1. ^ "Announcing BGV Summer 2013 Cohort!". Bethnal Green Ventures Blog. 24 June 2013. Retrieved 8 March 2020.
  2. ^ "Teams announced for Bethnal Green Ventures Summer 2013". Nesta. 24 June 2013. Archived from the original on 2013-07-07. Retrieved 7 July 2013.
  3. ^ "WriteLaTeX joining forces with Bethnal Green Ventures and Nesta". Overleaf Blog. 25 June 2013. Retrieved 8 March 2020.
  4. ^ "The Bethnal Green Ventures Incubator opens for entries". Startacus. 17 March 2013. Retrieved 8 March 2020.
  5. ^ "We're back!". Bethnal Green Ventures Blog. 14 February 2013. Retrieved 8 March 2020.
  6. ^ Miller, Paul (14 February 2013). "Bethnal Green Ventures — some good news". Paul Miller Blog. Retrieved 8 March 2020.
  7. ^ "And suddenly… it's almost DEMO DAY!". Bethnal Green Ventures Blog. 17 September 2013. Retrieved 8 March 2020.
  8. ^ Shepherd, Cameron (23 July 2014). "Digital Science Invests in London start-up WriteLaTeX". Digital Science News Blog. Retrieved 9 March 2020.
  9. ^ "Digital Science invests in WriteLaTeX". Research Information. 23 July 2014. Retrieved 9 March 2020.
  10. ^ Zhou, Larry (23 July 2014). "WriteLaTeX picks up funding to push its collaborative academic writing tool". VentureBeat. Retrieved 9 March 2020.
  11. ^ Page, Benedicte (24 July 2014). "Digital Science in WriteLaTeX investment". The Bookseller. Retrieved 9 March 2020.
  12. ^ "Nominet Internet Award winners 2014 revealed". Nominet. 3 July 2014. Retrieved 8 January 2020.
  13. ^ "Britain's Top 100 fastest-growing businesses 2018". SyndicateRoom. Retrieved 8 January 2020.
  14. ^ a b Perkel, Jeffrey M. (2020-03-31). "Synchronized editing: the future of collaborative writing". Nature. 580 (7801): 154–155. Bibcode:2020Natur.580..154P. doi:10.1038/d41586-020-00916-6. PMID 32235940.
  15. ^ Pain, Elisabeth (2018-04-30). "How to write your Ph.D. thesis". Science | AAAS. Retrieved 2020-06-11.
  16. ^ Donnelly, Lois (3 November 2015). "A breakdown of FOSS for students and researchers in academia". Opensource.com. Retrieved 2020-06-11.
  17. ^ "LaTeX im Browser: Overleaf und ShareLaTeX fusionieren". iX Magazin (in German). Retrieved 2020-06-11.
  18. ^ Kasioumis, Nikos; Brancolini, Valeria (2019). Forti, A.; Betev, L.; Litmaath, M.; Smirnova, O.; Hristov, P. (eds.). "Collaborative Scientific Authoring at CERN: A user-centered approach". EPJ Web of Conferences. 214: 07003. doi:10.1051/epjconf/201921407003. ISSN 2100-014X. S2CID 203696999.
  19. ^ "What is Overleaf?". supportcenter.ieee.org. Retrieved 2020-06-11.
  20. ^ "Write your article using Overleaf | Springer". www.springer.com. Retrieved 2020-06-11.
  21. ^ "Submit a LaTeX manuscript to a Springer journal using Overleaf". Springer Nature Support. Retrieved 2020-06-11.
  22. ^ "Overleaf and ShareLaTeX join forces to create community of two million". Research Information. 20 July 2017. Retrieved 18 November 2019.
  23. ^ "Overleaf and ShareLaTeX join forces to create community of two million". Society for Scholarly Publishing (SSP). 20 July 2017. Retrieved 8 March 2020.
  24. ^ a b "ShareLaTeX is now part of Overleaf". ShareLaTeX. Retrieved 8 March 2020.
  25. ^ "Merging SaaS Products In A User-Centered Way: A Case Study of Overleaf and ShareLaTeX (Conference entry)". SIGCHI. Retrieved 2021-06-01.
  26. ^ Reis, Paulo; Lees-Miller, John D.; Laqua, Sven (2021). "Merging SaaS Products in a User-Centered Way — A Case Study of Overleaf and ShareLaTeX". Extended Abstracts of the 2021 CHI Conference on Human Factors in Computing Systems. pp. 1–8. doi:10.1145/3411763.3443455. ISBN 9781450380959. S2CID 233987710. {{cite book}}: |website= ignored (help)

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