symmetrical difference

USAGE SUMMARY

The phrase "symmetrical difference" is correct and usable in written English.
It is typically used in mathematics and set theory to describe the set of elements that are in either of two sets but not in their intersection. Example: "The symmetrical difference between set A and set B includes all elements that are unique to each set."

✓ Grammatically correct

Science

Ecological Engineering

Applied Geography

BMC Evolutionary Biology

BioMed Research International

Human-verified examples from authoritative sources

Exact Expressions

4 human-written examples

Spatial analysis using GIS tools (intersection, symmetrical difference) was performed to analyse the spatio-temporal wetland changes.

Ecological Engineering

The GIS symmetrical difference tool was subsequently used to perform an overlay analysis for the individual woody vegetation elements in order to study the change trajectories and to obtain information about the woodlands that have remained unchanged (continuous), the ones that have disappeared (extinct), and the ones that have newly appeared in the landscape (recent).

Applied Geography

Then we calculated symmetrical difference for the gene trees with artificial transfers and normalized the obtained values by the average value of symmetric difference of the original data minus two standard deviations.

BMC Evolutionary Biology

Using the number of common and distinctive interacting members of the two proteins in an interaction network, PRODISTIN computes the functional distance using the Czekanovski-Dice distance formula [ 50], which reflects the symmetrical difference between the two proteins in an interaction network.

BioMed Research International

Human-verified similar examples from authoritative sources

Similar Expressions

56 human-written examples

Thus, if the artifact was symmetrical, the difference between the end tidal and arterial partial pressure during washout should be only about 1/5 of the difference during uptake (13% versus 55% difference).

BMC Anesthesiology

Other explanations are still possible: the ROC curve may not be unique or symmetrical 24 26; differences in the patient spectrum between the two populations may affect the different performance characteristics observed.

BMJ Open

Upon comparison of the lower face in the asymmetrical subjects against the lower face in the symmetrical subjects, the difference in the RMS error values was statistically significant (p < 0.0001).

Progress in Orthodontics

It can also be seen in Table 2 that although configurations 1 4 and configurations 5 7 are respectively symmetrical, there are differences in the classifier results.

Plosone

Therefore, it is likely that there is opportunity for reciprocal fitness affects between interacting native and exotic species, though these effects may not be entirely symmetrical, due to differences in both the frequency of interactions and the strength of competitive ability between native and invasive species.

Evolutionary Applications

They can also smell the difference between symmetrical and non-symmetrical faces.

Independent

However, since the intervals are constructed to be symmetrical about the mean difference, and not symmetrical about 0, the TDI could be constructed by taking the maximum of the absolute value among lower and upper limits: max(| L low |, | L upp |).

BMC Medical Research Methodology

Expert writing Tips

Best practice

Always define the sets or objects you are comparing when using "symmetrical difference" to avoid ambiguity.

Common error

Avoid using "symmetrical difference" when you simply mean the general difference between two things. This term has a specific mathematical meaning and should be used accurately.

Linguistic Context

The phrase "symmetrical difference" functions as a technical term, primarily used in mathematics and computer science. It denotes a specific operation between sets. Ludwig indicates its correctness and usability in written English.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "symmetrical difference" is a grammatically correct phrase primarily used in technical contexts, specifically within mathematics and set theory. Ludwig AI confirms its validity. Its function is to describe a specific mathematical operation, and its register is formal and scientific. Although it's a correct term, in non-technical contexts it may be better to use more general alternatives. While not very frequent, when used correctly, demonstrates an understanding of technical concepts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

symmetric difference

This alternative uses the more common spelling variant "symmetric" instead of "symmetrical".

exclusive or

This phrase describes the logical operation that "symmetrical difference" represents.

exclusive disjunction

This phrase, similar to "exclusive OR", focuses on the logical operation.

set difference

This alternative focuses on the mathematical operation relating to sets, which is "symmetrical difference" is a specific type.

disjunctive difference

This alternative emphasizes the disjunctive nature of the difference.

difference excluding the intersection

This alternative focuses on removing the common elements.

non-intersection elements

This phrase describes the elements that are not common to both sets.

elements unique to either set

This phrase is a descriptive way of expressing the outcome of the "symmetrical difference" operation.

distinctive elements between sets

This alternative highlights the distinctiveness of the elements in each set.

elements present in one set or the other, but not both

This is a detailed explanation of "symmetrical difference" using different wording.

FAQs

What is the meaning of "symmetrical difference" in set theory?

In set theory, "symmetrical difference" refers to the set of elements which are in either of the sets, but not in their intersection. It's the set of elements unique to each set.

Can I use "symmetric difference" instead of "symmetrical difference"?

Yes, "symmetric difference" is a more common and widely accepted variant of "symmetrical difference". Both terms refer to the same mathematical concept.

What is an alternative to "symmetrical difference" in non-mathematical contexts?

In non-mathematical contexts, you can use phrases like "distinct differences", "key differences", or "unique aspects" depending on the specific meaning you want to convey. These alternatives are less technical and more accessible to a general audience.

How does "symmetrical difference" differ from a simple difference?

"Symmetrical difference" specifically excludes the intersection of two sets, focusing only on elements unique to each set. A simple difference might refer to any kind of dissimilarity, not necessarily related to set theory. It is closely related to "exclusive OR".