different between corollary vs complementary

English

Etymology

From Middle English, from Late Latin cor?ll?rium (“money paid for a garland; gift, gratuity, something extra; consequence, deduction”), from cor?lla (“small garland”), diminutive of cor?na (“crown”).

Pronunciation

• IPA^(key): /k????l??i/, /?k???l??i/
• (US) enPR: kôr'?l?r?, IPA^(key): /?k????l??i/
• (General Australian) IPA^(key): /k???o??l??i/

Noun

corollary (plural corollaries)

1. Something given beyond what is actually due; something added or superfluous.
2. Something which occurs a fortiori, as a result of another effort without significant additional effort.

   Finally getting that cracked window fixed was a nice corollary of redoing the whole storefront.

3. (mathematics, logic) A proposition which follows easily from the proof of another proposition.

   We have proven that this set is finite and well ordered; as a corollary, we now know that there is an order-preserving map from it to the natural numbers.

Translations

Adjective

corollary (not comparable)

1. Occurring as a natural consequence or result; attendant; consequential.
2. (rare) Forming a proposition that follows from one already proved.

Further reading

• corollary in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• corollary in The Century Dictionary, New York, N.Y.: The Century Co., 1911.

English

Etymology

complement +? -ary

Pronunciation

• (Received Pronunciation) IPA^(key): /?k?mpl???m?nt(?)?i/
• (General American) enPR: k?m'pl?-m?n?t?-r?, -tr?, IPA^(key): /?k?mpl???m?nt(?)?i/
• Homophone: complimentary
• Rhymes: -?nt??i, -?nt?i
• Hyphenation: com?ple?men?ta?ry

Adjective

complementary (comparative more complementary, superlative most complementary)

1. Acting as a complement; making up a whole with something else.

   • Using the terminology we intro-
     duced earlier, we might then say that black and white squares are in comple-
     mentary distribution on a chess-board. By this we mean two things: firstly,
     black squares and white squares occupy different positions on the board: and
     secondly, the black and white squares complement each other in the sense that
     the black squares together with the white squares comprise the total set of 64
     squares found on the board (i.e. there is no square on the board which is not
     either black or white).

2. (genetics) Of the specific pairings of the bases in DNA and RNA.
3. (physics) Pertaining to pairs of properties in quantum mechanics that are inversely related to each other, such as speed and position, or energy and time. (See also Heisenberg uncertainty principle.)

Usage notes

• Complementary and complimentary are frequently confused and misused in place of one another.

Derived terms

Related terms

• complemental

Translations

Noun

complementary (plural complementaries)

1. A complementary colour.
2. (obsolete) One skilled in compliments.
3. An angle which adds with another to equal 90 degrees.

   (Can we find and add a quotation of Ben Jonson to this entry?)

Translations

Further reading

• complementary in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• complementary in The Century Dictionary, New York, N.Y.: The Century Co., 1911.