live on

To stay alive by eating or drinking a particular kind of food or drink.

• You cannot live on sweets alone.
• They lived on rice and beans during the winter.
• What do these tiny animals live on?

How to use it: live on something (The stranded hikers lived on berries for several days.)

Similar words: subsist on, survive on

Common phrases: live on something, live on rice

To pay for your needs using a particular amount or source of money.

• We live on my salary.
• He lived on his savings while looking for work.
• Could you live on that much money each month?

How to use it: live on something (She lives on a small pension.)

Similar words: get by on, subsist on

Common phrases: live on something, live on savings

To continue to exist or be remembered after a death or after a long time.

• Her memory lives on.
• The old traditions lived on in remote villages.
• His music will live on long after his death.

How to use it: live on in/through something (His memory lives on in the stories his children tell.)

Similar words: endure, survive, last

Opposites: disappear

Common phrases: live on forever, live on through something

If a mathematical function exists on a particular set or space, that is where its inputs belong.

• The function lives on the real line.
• These functions live on a curved surface.
• Which space does this mathematical object live on?

How to use it: live on a set/space (This function lives on the unit interval.)

Similar words: be defined on

Common phrases: live on something, live on manifolds