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The phrase "a finite upper bound" is correct and usable in written English.
It can be used in mathematical or technical contexts to describe a limit that is both finite and serves as an upper boundary for a set of values.
Example: "In this analysis, we established a finite upper bound for the maximum allowable error in our calculations."
Alternatives: "a limited upper boundary" or "a defined maximum limit".
Exact(7)
In this contribution, it is shown that for a given number density of particles in a microstructure of infinite extent, there exists a finite upper bound on the mean first nearest neighbour distance.
However, when we are dealing with a variable which has a finite upper bound, a modified version is called for.
In this paper, we are investigating the ability of a sending node to get access to the channel within a finite upper bound.
Erreygers and Van Ourti [6] pointed out that the use of the health Concentration Index is pertinent when we are dealing with a ratio-scale health variable which is unbounded, i.e. which does not have a finite upper bound.
Multiplying by −1 and taking into account the fact that both ω ( t ) and p α ( σ ( t ) ) φ ( t ) τ ′ ( t ) v ( t ) are nonnegative we get a finite upper bound for the integral from (15), which contradicts (15).
In his supertask, while the accelerated observer O* will have a finite upper bound on the proper time elapsed on his world-line, there will be no event on his world-line from which he can look back and see an infinity of time elapsed along the world-line of some unaccelerated observer.
Similar(53)
In particular, the predictive controller can compensate transmission delays with any finite upper bound under the constraint that the sampling periods of the plant output and the observer output are small enough as well as the constraint that the predictor is accurate enough.
There is a small finite upper bound on the amount of easily accessible water in near-Earth space, including water from C-type NEAs and permanently shadowed lunar craters.
Statistically improper priors, such as intervals extending to infinity, were converted to proper priors with a large, finite upper bound.
This finite upper bound on in STDMA does, however, come at the expense of increased interference on the channel (i.e., more packet collisions in the air will occur) as compared with CSMA.
It is easy to see that any nonempty finite subset of has a least upper bound, denoted by sup .
More suggestions(15)
a calculated upper bound
a realistic upper bound
a new upper bound
a trivial upper bound
a rough upper bound
a simple upper bound
a general upper bound
a tight upper bound
a positive upper bound
a hard upper bound
a posteriori upper bound
a finite outer bound
a true upper bound
a negative upper bound
a nontrivial upper bound
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com