Adjective
Lacking dimensions.
Usage- not-comparable
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To Heav'n thir prayers / Flew up, nor miſsd the way, by envious windes / Blow'n vagabond or fruſtrate: in they paſsd / Dimentionleſs through Heav'nly dores; […]
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Extended objects may be separated by dimensionless points; but dimensionless points cannot be separated, but by some real distance, or something really extended.
1930, E. E. Smith, Skylark Three, Fantasy Press, 1948, Chapter 3, They saw the utter, absolute darkness of the complete absence of all light; and upon that indescribable blackness they beheld superimposed the almost unbearable brilliance of enormous suns concentrated into mathematical points, dimensionless.
He did not look once again toward the dark house. […] He simply went quietly as if that were his natural manner of moving and passed around the now dimensionless bulk of the house, toward the rear, where the kitchen would be.
Of a physical constant: lacking units.
Usage- not-comparable
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Iron has a density of 7.8 grams per cubic centimeter: its dimensionless relative density is 7.8.
More examples (1)
A strain is a dimensionless quantity and is usually expressed in percentages. Typical measures for strain are less than 2 mm/m for steel and are often expressed in micro-strain units. One microstrain is the strain producing deformation of one part per million.