different between ease vs smoothness

English

Etymology

From Middle English ese, ays, etc., from Anglo-Norman ese (“ease”), from Old French eise and aise (“elbow room; opportunity”), of uncertain and obscure origin. Cognate with Provencal ais, Italian agio and asio, and Portuguese azo. Sometimes ascribed to Latin *asia or *asium, possibly from ansa (“handle; occasion”) but more likely from a Vulgar Latin *adjace(m), from Latin adjac?ns, present participle of adjace?. Alternatively, possibly from a non-Latin source such as Germanic or Celtic on the basis of the conflicting forms which appear in various Romance languages. Compare Old English ?eþe (“easy”), Gothic ???????????????????? (az?ti, “ease; pleasure”), *???????????????????? (*az?ts, “easy”), Breton eaz, ez (“easy”), Irish adhais (“easy; leisure”). Compare also Frankish *ansiju (“loophole, eyelet; handle, arms akimbo, elbow room”). See also eath.

The verb is from Middle English esen, ultimately of the same origin.

Pronunciation

• (UK) IPA^(key): /i?z/
• (US) enPR: ?z, IPA^(key): /iz/,
• Rhymes: -i?z
• Homophones: ees, E's, 'e's

Noun

ease (uncountable)

1. Ability, the means to do something, particularly:
   1. (obsolete) Opportunity, chance.
      • a. 1200, Ancrene Riwle (Cleopatra MS C.vi), p. 213:

        ...?ef þer is eise to fulle þe dede...

   2. Skill, dexterity, facility.

2. Comfort, a state or quality lacking unpleasantness, particularly:
   1. Freedom from pain, hardship, and annoyance, sometimes (derogatory, archaic) idleness, sloth.

   2. Freedom from worry and concern; peace; sometimes (derogatory, archaic) indifference.

   3. Freedom from difficulty.

   4. Freedom from effort, leisure, rest.

   5. Freedom from financial effort or worry; affluence.

   6. Freedom from embarrassment or awkwardness; grace.

3. Relief, an end to discomfort, particularly:
   1. Followed by of or from: release from or reduction of pain, hardship, or annoyance.

   2. (euphemistic, obsolete) Release from intestinal discomfort: defecation.
   3. Release from constraint, obligation, or a constrained position.

   4. (clothing) Additional space provided to allow greater movement.

4. (obsolete) A convenience; a luxury.
5. (obsolete) A relief; an easement.

Synonyms

• (ability): ability, dexterity, facility, skill
• (comfort): comfort, peace
• (freedom from worry): peace of mind
• (freedom from effort): free time, leisure, relaxation, rest

Derived terms

Related terms

• easy, easiness

Translations

Verb

ease (third-person singular simple present eases, present participle easing, simple past and past participle eased)

1. (transitive) To free (something) from pain, worry, agitation, etc.
   • Elyse Saugstad, a professional skier, wore a backpack equipped with an air bag, a relatively new and expensive part of the arsenal that backcountry users increasingly carry to ease their minds and increase survival odds in case of an avalanche.

2. (transitive) To alleviate, assuage or lessen (pain).

3. (transitive) To give respite to (someone).
4. (nautical, transitive) To loosen or slacken the tension on a line.

5. (transitive) To reduce the difficulty of (something).

6. (transitive) To move (something) slowly and carefully.

7. (intransitive) To lessen in severity.

8. (intransitive) To proceed with little effort.

Synonyms

• (free (something) from pain, worry, agitation, etc): assuage, salve
• (alleviate, assuage or lessen (pain)): allay, alleviate, assuage, lessen, reduce
• (give respite to (someone)): give someone a break (informal), lay off (informal)
• (loosen or slacken the tension on (something)): loosen, relax, slacken
• (reduce the difficulty of (something)): facilitate, simplify
• (lessen in severity): lessen, reduce
• (proceed with little effort): cruise

Translations

References

Middle English

Noun

ease (plural eases)

1. Alternative spelling of ese

English

Etymology

From Middle English smethnes, *smothnes, from Old English sm?þnes, *sm?þnes (“smoothness, a smooth place, a level surface”), equivalent to smooth +? -ness.

Noun

smoothness (countable and uncountable, plural smoothnesses)

1. The condition of being smooth; the degree or measure of said condition.
   • 1998, Vladimir V. Senatov, Normal Approximation: New Results, Methods and Problems, Walter de Gruyter (VSP), page 32,

     The ‘smoothness’ of distributions can be understood in various senses, this is why we used quotation marks before; further we will drop them. The smoothness can be understood as the differentiability of the distribution function, boundedness of some of its derivatives, the existence of the absolutely continuous component, the decrease of the characteristic function with a certain rate, the validity of the Cramér condition, the condition ${\displaystyle \sigma (\Phi )\rightarrow 0}$ as ${\displaystyle n\rightarrow \infty }$, etc.

   • 2013, Robert Otto Rasmussen, et al., Real-time Smoothness Measurements on Portland Cement Concrete Pavements During Construction, Transportation Research Board, page 3,

     With it,^{[a pavement profile]} paving operations can be adjusted "on the fly" to maintain or improve smoothness.

2. (mathematical analysis, of a function) The highest order of derivative (the differentiability class) over a given domain.

3. (approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness.
   • 2013, Feng Dai, Yuan Xu, Approximation Theory and Harmonic Analysis on Spheres and Balls, Springer, page 79,

     A central problem in approximation theory is to characterize the best approximation of a function by polynomials, or other classes of simple functions, in terms of the smoothness of the function. In this chapter, we study the characterization of the best approximation by polynomials on the sphere. In the classical setting of one variable, the smoothness of a function on ${\displaystyle \mathbb {S} ^{1}}$ is described by the modulus of smoothness, defined by the forward difference.

Antonyms

• (condition of being smooth): jerkiness, roughness

Derived terms

• modulus of smoothness

Translations

See also

• differentiability class
• modulus of continuity
• modulus of smoothness
• uniform continuity

Further reading

• Modulus of smoothness on Wikipedia.Wikipedia
• Modulus of continuity on Wikipedia.Wikipedia