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in the limit vs on the limit

Both 'in the limit' and 'on the limit' are correct, but they are used in different contexts. 'In the limit' is commonly used in mathematics to describe a situation as it approaches a certain value or condition. 'On the limit' is more commonly used in sports or other activities to describe being at the maximum or extreme point of performance.

Last updated: March 21, 2024

in the limit

This phrase is correct and commonly used in mathematics to describe a situation as it approaches a certain value or condition.

This phrase is typically used in mathematical contexts to describe the behavior of a function or sequence as it approaches a certain value or condition.

Examples:

In the limit as x approaches infinity, the function approaches zero.
The speed of the car tends to zero in the limit as time goes to infinity.

Show examples from the web [+]

Language identification in the limit is a formal model for inductive inference. It was introduced by E. Mark Gold in his paper with the same title In this model, ...
In computability theory, a function is called limit computable if it is the limit of a uniformly computable sequence of functions. The terms computable in the limit ...
INFORMATION AND CONTROL 10, 447—474 '(1967). Language Identiﬁcation in the Limit. E MARK G0L1)*. The RAND Corporation. Language learnability has ...
@article{gold67limit, author={E. Mark Gold}, title={Language identification in the limit}, journal={Information and Control}, year={1967}, volume={10}, number={5} ...

Alternatives:

as the limit approaches
approaching the limit
as the value approaches the limit
as it approaches the limit
as the condition approaches the limit

on the limit

This phrase is correct and commonly used in sports or other activities to describe being at the maximum or extreme point of performance.

This phrase is typically used in contexts related to sports or other activities to describe being at the maximum or extreme point of performance.

Examples:

He was pushing himself to the limit during the race.
The athlete was on the limit of his physical abilities.

Show examples from the web [+]

On The Limit. Services · Catalogs · FAQ · Blog · Get a Quote · Request a Reorder · Merchandise · Login · Create Account. Submit. Contact Us. slide 1 ...
On The Limit · Services · Catalogs · FAQ · Blog · Get a Quote · Request a Reorder · Merchandise · Login · Create Account. Submit. Contact Us ...
Despite production starting before either of the former films, 1: Life on the Limit is the last to be released, and suffers a little because of it. I had the privilege of ...
Jan 6, 2014 ... In Cinemas January 10th. Narrated by Michael Fassbender, 1: Life On The Limit is an action-packed, cinematic documentary that channels the ...

Alternatives:

at the limit
pushing the limit
at the maximum performance level
at the extreme point of performance
at the peak of performance

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