upper and lower bounds

USAGE SUMMARY

"upper and lower bounds" is a correct and commonly used phrase in English.
It is used in a sentence to refer to the highest and lowest possible values or limits that apply to a particular situation or context. Example: The company has set upper and lower bounds for the budget, ensuring that expenses do not exceed $10,000 or fall below $8,000.

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Some sort of estimate for good upper and lower bounds.

Yale University

Case study on forging: upper and lower bounds.

Princeton University

However, the upper and lower bounds are assumed unknown.

Systems & Control Letters

We derive sharp upper and lower bounds for both parameters.

Theoretical Computer Science

Upper and lower bounds on these errors is also provided.

Computers & Operations Research

(Upper and lower bounds are +/− robust standard errors from the mean clustered on session).

Nature

For finding strings of Hamming distance 1, we have upper and lower bounds that match exactly.

Stanford University

(using lim sup and lim inf for upper and lower bounds as appropriate).

University of California, Berkeley

Furthermore, upper and lower bounds of the performance measures can be computed.

University of California, Berkeley

Thus, these two values are upper and lower bounds, respectively, of π.

Encyclopedia Britannica

(Upper and lower bounds are +/− robust standard errors clustered on double-pairs; see SI Section 2 for statistical details).

Nature

Expert writing Tips

Best practice

When defining a range, explicitly state the "upper and lower bounds" to avoid ambiguity. For example, "The acceptable temperature range has upper and lower bounds of 20°C and 10°C respectively."

Common error

Avoid using "upper and lower bounds" when you actually mean estimates or approximations. Bounds define a guaranteed range, while estimates suggest a likely value.

Linguistic Context

The phrase "upper and lower bounds" functions as a noun phrase, often serving as a subject or object in a sentence. It refers to the maximum and minimum values within which a measurement or calculation is expected to lie. Ludwig confirms this usage is grammatically sound.

Expression frequency: Very common

Frequent in

Science

50%

Academia

40%

Formal & Business

5%

Less common in

News & Media

3%

Encyclopedias

1%

Wiki

1%

Ludwig's WRAP-UP

In summary, "upper and lower bounds" is a grammatically correct and very common phrase used to define a range of possible values. Ludwig AI confirms its validity and frequent use in academic and scientific contexts. It is mostly found in science and academia. When using the phrase, ensure you're defining a guaranteed range, not just an estimate. Consider using alternatives like "maximum and minimum values" or "limiting values" depending on the specific context. It's important to clearly articulate "upper and lower bounds" to avoid ambiguity and provide a clear framework for analysis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

maximum and minimum limits

Focuses on the extreme values within a set, emphasizing the quantitative aspect of the range.

highest and lowest values

Directly refers to the extreme data points, suitable for statistical or data-driven contexts.

extreme boundaries

Highlights the outermost limits, often used in discussions of spatial or abstract extents.

limiting values

Emphasizes the role of these values as constraints or restrictions on a system or variable.

range of possibilities

Shifts the focus to the spectrum of potential outcomes or values between the limits.

interval of uncertainty

Highlights the uncertainty in a measure.

confidence interval

Highlights the statistical confidence in a measure.

acceptable thresholds

Introduces the notion of acceptability, implying a judgment about what is permissible within the limits.

outer limits

Emphasizes the distance from a central point, often used in the context of tolerance or capacity.

maximum and minimum extent

Refers to the full scope or scale, suitable for contexts involving physical dimensions or abstract magnitudes.

FAQs

How do I use "upper and lower bounds" in a sentence?

Use "upper and lower bounds" to define the range within which a value or quantity is expected to fall. For example, "The simulation provided "upper and lower bounds" for the project's cost."

What's the difference between "upper and lower limits" and ""upper and lower bounds""?

The terms are often used interchangeably, but ""upper and lower bounds"" might imply a more rigorous or mathematically defined range, while "upper and lower limits" can be more general.

What can I say instead of ""upper and lower bounds""?

You can use alternatives like "maximum and minimum values", "range of values", or "limiting values" depending on the context.

In what fields is the phrase ""upper and lower bounds"" commonly used?

The phrase ""upper and lower bounds"" is commonly used in mathematics, statistics, engineering, and economics to define the limits within which a value or quantity is expected to fall.