inverse to each other

USAGE SUMMARY

The phrase "inverse to each other" is correct and usable in written English.
It can be used to describe a relationship where two elements have opposite effects or characteristics. Example: "In mathematics, the functions sine and cosine are often considered inverse to each other."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

The two constructions are inverse to each other (nowadays this is known as the Grothendieck construction).

Bulletin of Mathematical Sciences

end{aligned}Indeed, it can be checked that the assignments begin{aligned}&varphi _1, :, s longmapsto s_0, t longmapsto t&varphi _2, :, s_i longmapsto s^{t^i}, t longmapsto tquad (0 le i le n) end{aligned}define, between the groups of the two previous presentations, isomorphisms that are inverse to each other.

Bulletin of Mathematical Sciences

For the simplest case of a multiconductor TL system in a homogeneous medium [20] the per-unit-length inductance and capacitance matrices are up to a constant inverse to each other: mathbf{L}mathbf{C}=frac{1}{c_{l}^{2}}mathbf{1}, (11) where 1 is the (ntimes n) identity matrix.

EPJ Quantum Technology

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

The proof is achieved by Theorem 5 and the previously proved fact that the new fractional sums and differences are the inverses to each other.

Advances in Difference Equations

Not only, he says, are politics and literature "in an inverse relationship to each other", they are in an antagonistic relationship.

The Guardian

"Prominence and influence are in inverse proportions to each other," he told The New York Times in 1978.

The New York Times

After all, art is all the things that politics isn't: "Politics is the great generaliser and literature the great particulariser," wrote Philip Roth, "and not only are they in an inverse relationship to each other – they are in an antagonistic relationship.

The Guardian

However, they stand in a variable and inverse relationship to each other, where the relative preponderance of one function is offset by the relative subordination of the remaining ones, but at no time can any particular function be cancelled out altogether (ST, p. 98).

SEP

Therefore, their subsitution ratios are in inverse proportion to each other: S X = 1/ S nonX.

BMC Genomics

Only the length of the expanded CAG and age at onset showed a strong inverse relationship to each other [ 62, 67].

BioMed Research International

On both sides of the lacZα fragment two different type IIS recognition sequences - here BsaI and BpiI - are positioned in inverse orientation relative to each other, but creating the identical fusion site as exemplified by plasmid pL0-P in figure 3.

Plosone

Expert writing Tips

Best practice

When using the phrase "inverse to each other", ensure that the context clearly establishes the two elements being compared and their relationship. For example, specify the variables or functions involved.

Common error

Avoid assuming that "inverse to each other" implies a simple negation. Ensure that the relationship is truly an inverse one, where one element counteracts or reverses the effect of the other, and not just different.

Linguistic Context

The phrase "inverse to each other" functions primarily as a prepositional phrase, often used to modify a verb or noun, indicating a relationship of opposition or reversal between two entities. Ludwig AI confirms the usage in scientific contexts.

Expression frequency: Rare

Frequent in

Science

75%

News & Media

25%

Formal & Business

0%

Less common in

Encyclopedias

0%

Wiki

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, the phrase "inverse to each other" is a grammatically sound and usable prepositional phrase that describes a reciprocal relationship between two entities. As shown by Ludwig AI, it is most frequently used in scientific and formal contexts. While "inverse to each other" is a valid way to express inverse relations, it is recommended to use alternatives like "reciprocal to each other" or "opposite to each other" to enhance clarity. Remember to use it precisely, ensuring that the inverse relationship is clear and well-defined.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

reciprocal to each other

Implies a mathematical or proportional relationship where one value decreases as the other increases, or vice versa, maintaining a constant product.

opposite to each other

Indicates a direct contradiction or contrast in nature, direction, or effect.

contrary to each other

Suggests a conflict or incompatibility between two things, differing in opinion or action.

in opposition to each other

Highlights a state of conflict or resistance between two entities.

diametrically opposed to each other

Emphasizes the extreme divergence or opposition between two viewpoints or positions.

reverse of each other

Focuses on the idea that one is the mirror image or exact opposite of the other.

antithetical to each other

Indicates a fundamental and irreconcilable opposition.

complementary to each other

Describes a relationship where two things complete or enhance each other, though potentially opposite in nature.

in an inverse relationship

Highlights the overall correlation between two elements or concepts.

functions inversely

Emphasizes the action of the relation more than the relation itself

FAQs

How can I use "inverse to each other" in a sentence?

You can use "inverse to each other" to describe two elements that have opposite effects. For example: "In a seesaw, the positions of each side are "inverse to each other"."

What's a good alternative to "inverse to each other"?

Depending on the context, you could use "opposite to each other", "reciprocal to each other", or "in an inverse relationship".

Is it correct to say 'inversely proportional to each other' instead of "inverse to each other"?

While "inversely proportional" implies a specific mathematical relationship, "inverse to each other" is a more general term. Choose based on the precision needed. For instance "inversely proportional to each other" is better suited for equations, for more general context the main query is better

When is it appropriate to use "inverse to each other" in writing?

Use "inverse to each other" when you want to emphasize that two things have opposite or reverse effects on each other. For general correlation use "in an inverse relationship".