the assertion that there is no set whose cardinality is greater than that of the integers and smaller than that of the reals
continuum hypothesis in American English
noun
Math
a conjecture of set theory that the first infinite cardinal number greater than the cardinal number of the set of all positive integers is the cardinal number of the set of all real numbers
Word origin
[1935–40]This word is first recorded in the period 1935–40. Other words that entered Englishat around the same time include: blitz, complementation, fluorocarbon, unit trust, walk-through
Examples of 'continuum hypothesis' in a sentence
continuum hypothesis
At the fundamental level, this exploration will test the continuum hypothesis beyond memory.
Mélanie eBrion, Anne-Lise ePitel, Hélène eBeaunieux, Pierre eMaurage 2014, 'Revisiting the continuum hypothesis: towards an in-depth exploration of executivefunctions in Korsakoff syndrome.', Frontiers in Human Neurosciencehttp://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00498/full. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
To explain our findings, we propose a continuum hypothesis of vocal learning.
Gustavo Arriaga, Eric P Zhou, Erich D Jarvis 2012, 'Of mice, birds, and men: the mouse ultrasonic song system has some features similarto humans and song-learning birds.', PLoS ONEhttp://europepmc.org/articles/PMC3468587?pdf=render. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Secondly, from the acoustic modeling point of view, one faces the limit of validity of the continuum hypothesis.
Alain Glière, Justin Rouxel, Mickael Brun, Bertrand Parvitte, Virginie Zéninari, SergioNicoletti 2014, 'Challenges in the Design and Fabrication of a Lab-on-a-Chip Photoacoustic Gas Sensor',Sensorshttp://www.mdpi.com/1424-8220/14/1/957. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this perspective, applying the dual-process model to binge drinking might renew the understanding of this continuum hypothesis.
Severine eLannoy, Joël eBillieux, Pierre eMaurage 2014, 'Beyond inhibition: A dual-process perspective to renew the exploration of binge drinking.',Frontiers in Human Neurosciencehttp://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00405/full. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)