Extremally vs. Extremely: What's the Difference?
"Extremally" is a rare term used in mathematics, while "extremely" is an adverb meaning to a very high degree.
"Extremally" is a term most commonly used in a mathematical context, particularly in topology, to describe a property related to the extreme points of a set. "Extremely," on the other hand, is a common adverb in English that is used to emphasize the high degree of a particular quality or state.
In the realm of geometry, "extremally" might be used to discuss points that are extreme in the context of convex sets. "Extremely," however, can be used in everyday language to intensify adjectives, such as in "extremely happy" or "extremely cold."
"Extremally" does not see frequent use outside of technical or mathematical discussions, making it less familiar to the general public. "Extremely" is widely recognized and used to convey the utmost degree or to signify that something is being done to a great extent.
One would encounter "extremally" in academic papers or discussions focusing on mathematical theories. In contrast, "extremely" is part of everyday vocabulary and is often used to express strong emotions or conditions.
Since "extremally" is so specialized, it lacks the broad applicability that "extremely" has, which serves as a universal intensifier in the English language.
Pertaining to extreme points in mathematics
Signifying a high degree or intensity
Technical, mathematical contexts
General language to intensify adjectives/adverbs
Used in academic or scientific papers
Used in everyday conversation and writing
Describes mathematical concepts or relationships
Modifies adjectives and adverbs to provide emphasis
Extremally and Extremely Definitions
Refers to the behavior or properties at the extreme ends of a spectrum.
The study focused on the extremally high frequencies of the wave.
To a very great degree; exceedingly.
She was extremely excited about her birthday party.
In optimization, pertaining to the solutions on the boundary of the feasible region.
The algorithm searches for an extremally optimal point.
Used to emphasize the seriousness of something.
The weather conditions were extremely dangerous.
Used in the context of extremal combinatorics, a branch of mathematical theory.
They published a paper on extremally large combinatorial structures.
Signifying something that is done to a high intensity.
He was extremely focused on his research.
Concerning the outermost boundaries in geometrical shapes.
This theorem identifies an extremally bounded region in the plane.
Expressing an action or quality taken to its utmost point.
The test was extremely difficult for everyone.
Related to the extreme points or elements of a set in topology.
The function was examined for its extremally discrete properties.
Denoting the highest degree of a quality or state.
The opera singer was extremely talented.
To an extremal extent
Most remote in any direction; outermost or farthest
The extreme edge of the field.
Being in or attaining the greatest or highest degree; very intense
Being far beyond the norm
An extreme conservative.
Of the greatest severity; drastic
Took extreme measures to conserve fuel.
Characterized by severe, usually oxygen-poor environmental conditions.
Having an affinity for such conditions
An extreme microorganism.
Very dangerous or difficult
Participating or tending to participate in a very dangerous or difficult sport
An extreme skier.
(Archaic) Final; last.
The greatest or utmost degree or point.
Either of the two things situated at opposite ends of a range
The extremes of boiling and freezing.
An extreme condition.
An immoderate, drastic expedient
Resorted to extremes in the emergency.
The first or last term of a ratio or a series.
A maximum or minimum value of a function.
(Logic) The major or minor term of a syllogism.
(degree) To an extreme degree.
In an extreme manner or state; in the utmost degree; to the utmost point; exceedingly; as, extremely hot or cold.
To a high degree or extent; favorably or with much respect;
He spoke highly of her
Does not think highly of his writing
To an extreme degree;
To an extreme degree;
The house was super clean for Mother's visit
To an extreme degree or extent;
His eyesight was exceedingly defective
What does "extremally disconnected space" mean?
It's a term in topology referring to a space where closures of open sets are open.
Is "extremally" commonly used in English?
No, it's primarily used in mathematical contexts.
Are there synonyms for "extremely"?
Yes, words like "incredibly" and "exceptionally" are synonyms.
Is it correct to say "extremely more"?
No, "extremely" should be followed by an adjective or adverb, not a comparative form.
Can "extremely" be used in formal writing?
Yes, it's suitable for both formal and informal contexts.
Can "extremely" modify any adjective?
It can modify most adjectives and adverbs, especially those pertaining to degree or intensity.
Is "extremally" recognized in all areas of mathematics?
It's specific to certain areas, like topology and convex analysis.
What's a layman's term for "extremally"?
There isn't a layman's term; it's a technical mathematical term.
Does "extremally" have a different meaning in different math fields?
Yes, its meaning can vary slightly depending on the context.
Are there any common mistakes when using "extremely"?
It's often incorrectly used with adjectives that are absolutes, like "unique."
Does "extremally" have an antonym?
Not specifically; its opposite would be context-dependent in mathematics.
How can I replace "extremely" to reduce repetition in writing?
Use varied intensifiers like "particularly," "especially," or "highly."
Is "extremally" ever used outside of math?
It's rare and typically not found outside specialized academic writing.
How does "extremely" compare with "very"?
"Extremely" indicates a higher degree of intensity than "very."
What's the best way to learn the use of "extremely"?
Through reading and listening to the word used in various sentences to understand its intensity.
In what contexts should "extremely" be avoided?
When a more precise or less exaggerated term is required.
Can "extremely" be used to describe a negative situation?
Yes, it can intensify both positive and negative descriptions.
Is "extremally" part of standard English dictionaries?
It's not commonly found in general English dictionaries due to its specialized use.
What is an "extremal element"?
In mathematics, it's an element of a set that is not surpassed within a certain order.
Can "extremely" be used in scientific writing?
Yes, when emphasizing a significant degree of a measurable quantity.
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