upper set

USAGE SUMMARY

The phrase "upper set" is correct and usable in written English.
It can be used in mathematical contexts, particularly in set theory, to refer to a set that contains all elements greater than or equal to a certain value. Example: "In the context of real numbers, the upper set of a given number includes all numbers greater than or equal to that number."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Wiki

Human-verified examples from authoritative sources

Exact Expressions

27 human-written examples

There were prominent upper and lower tusklike teeth at the front of the mouth (the upper set in the premaxillary bones, the lower on the dentary bones).

Encyclopedia Britannica

We also design incremental algorithms to compute the second and sixth lower and upper set approximations.

Information Sciences

Table 1 (upper set) reports some structural characteristics for all the systems enumerated earlier.

Nanoscale Research Letters

The upper set of curves presents the results for room temperature, while the lower ones for 140°C.

Nanoscale Research Letters

Note that by definition, the systemic risk measure is an upper set in the sense that all points above the boundary are acceptable.

Probability, Uncertainty and Quantitative Risk

We use a dashed black line to denote thiscommon boundary in Figure 3C (by arbitrary convention, we colorthe dashed line to match the upper set).

The Journal of Mathematical Neuroscience

Human-verified similar examples from authoritative sources

Similar Expressions

33 human-written examples

As a Harburg-Arlen parody of the play observed, a couple of years later, "We're living in the smart upper sets.

The New Yorker

Also, here the conditioning events, the lower and upper sets, have fixed probabilities α, while the δ indicator comprises an expectation over the conditioning variables.

BMC Systems Biology

Since we are interested in maximizing the pulse area, we used the parameter densities conditioned on the upper sets, and chose as conditioning values the corresponding modes.

BMC Systems Biology

Additional file 2: Figure S2 shows the λ, k12 and K2 lower and upper sets probability density for all the realizations and it confirms the low variability of the probability density shapes over the parameter space sampling.

BMC Systems Biology

PULL MY DAISY This short film from 1959 is a neat Beat picker-upper set in the slaphappy bohemian pad of a railroad conductor whose pals include Allen Ginsberg, Peter Orlovsky, and Gregory Corso — all of whom carry on, naturally enough, like poets in their youth.

The New Yorker

Expert writing Tips

Best practice

When using "upper set" in mathematical or scientific writing, clearly define the ordering or relation that determines which elements are 'above' others. For example, in set theory, an "upper set" is a subset of a partially ordered set that contains all elements greater than or equal to any element in the subset.

Common error

Avoid using "upper set" interchangeably with "upper bound". An upper bound is a single value that is greater than or equal to all elements in a set, while an "upper set" is a collection of such values.

Linguistic Context

The phrase "upper set" primarily functions as a noun phrase, typically within mathematical or scientific contexts. Ludwig provides examples demonstrating its use in defining subsets with specific properties in relation to ordered sets, and according to Ludwig AI the phrase is usable in written English.

Expression frequency: Uncommon

Frequent in

Science

75%

News & Media

13%

Wiki

6%

Less common in

Encyclopedias

6%

Formal & Business

0%

Reference

0%

Ludwig's WRAP-UP

The term "upper set" is a noun phrase primarily used in mathematical and scientific contexts to define subsets with specific properties in ordered sets. While grammatically correct, its usage is relatively uncommon outside of these technical domains. As Ludwig shows, it's important to differentiate it from related terms like "upper bound", and to define the underlying ordering or relation clearly when using it. Ludwig AI confirms its proper usability in the appropriate context. The authoritative sources citing this phrase are mainly scientific publications and encyclopedias.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

highest set

Directly indicates the set with the greatest elements or properties.

higher set

A simpler way to refer to the upper elements or values group.

top set

A simpler way to refer to the upper section or group.

upper bound

Focuses on the highest possible value within a set, rather than the set itself.

super set

Implies a set containing all elements of another set, which can be related to an upper set in certain contexts.

maximum set

Describes a set with the maximum elements values or properties.

maximal set

Refers to a set that cannot be extended without losing a specific property, similar to the idea of an upper limit.

greater set

Refers to a set composed by elements greater than a specific value.

superior set

Emphasizes the set's position above others in a hierarchy or ordering, akin to the 'upper' aspect.

elevated set

Refers to a set on an elevated position.

FAQs

What does "upper set" mean in mathematics?

In mathematics, specifically in order theory, an "upper set" is a subset of a partially ordered set that contains all elements greater than or equal to any element in the subset. It's closely related to the concept of an "upper bound".

How does an "upper set" differ from a lower set?

An "upper set" contains elements greater than or equal to its members, while a lower set contains elements less than or equal to its members. They are dual concepts in order theory.

In what contexts is it appropriate to use the term "upper set"?

The term "upper set" is appropriate in mathematical contexts, particularly in discussions of partially ordered sets, lattice theory, and related fields. It is less common in general language.

What are some alternatives to the term "upper set"?

Depending on the specific context, alternatives to "upper set" include "upper bound", "maximal set", or a descriptive phrase such as 'set of all elements greater than a certain value'.