live on

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live on (third-person singular simple present lives on, present participle living on, simple past and past participle lived on)

1. (idiomatic, intransitive) To endure.

   Her memory lives on in our hearts.

   • 2012 June 4, Lewis Smith, “Queen’s English Society says enuf is enough, innit?: Society formed 40 years ago to protect language against poor spelling and grammar closes because too few people care”, in The Guardian‎, London, archived from the original on 10 March 2016:

     He described the members and organisers of the society as "a group of enthusiasts celebrating the richness and diversity of the English language", and is convinced that whether or not enough volunteers can be found to keep the society going, their enthusiasm and love for good English will live on.

2. (idiomatic, transitive) To survive solely by consuming a certain thing.

   When he was in the rainforest, he lived on bugs and rainwater.

3. (transitive) To rely on financially.

   She lives on a stipend from her parents.

4. (mathematics, idiomatic, transitive) To be defined on.
   • 2018, Lars Ljungqvist and Thomas J. Sargent, Recursive Macroeconomic Theory, fourth edition, MIT Press, page 116:

     Let assets live on the grid ${\displaystyle {\mathcal {A}}=}$.

• live off

• in love, love-in