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 for Reduction ascending
From The Collaborative International Dictionary of English v.0.48 :

  Reduction \Re*duc"tion\ (r[-e]*d[u^]k"sh[u^]n), n. [F.
     r['e]duction, L. reductio. See Reduce.]
     1. The act of reducing, or state of being reduced; conversion
        to a given state or condition; diminution; conquest; as,
        the reduction of a body to powder; the reduction of things
        to order; the reduction of the expenses of government; the
        reduction of a rebellious province.
        [1913 Webster]
     2. (Arith. & Alg.) The act or process of reducing. See
        Reduce, v. t., 6. and To reduce an equation, To
        reduce an expression, under Reduce, v. t.
        [1913 Webster]
     3. (Astron.)
        (a) The correction of observations for known errors of
            instruments, etc.
        (b) The preparation of the facts and measurements of
            observations in order to deduce a general result.
            [1913 Webster]
     4. The process of making a copy of something, as a figure,
        design, or draught, on a smaller scale, preserving the
        proper proportions. --Fairholt.
        [1913 Webster]
     5. (Logic) The bringing of a syllogism in one of the
        so-called imperfect modes into a mode in the first figure.
        [1913 Webster]
     6. (Chem. & Metal.) The act, process, or result of
        reducing[7]; as, the reduction of iron from its ores; the
        reduction of an aldehyde into an alcohol.
        [1913 Webster]
     7. (Med.) The operation of restoring a dislocated or
        fractured part to its former place.
        [1913 Webster]
     Reduction ascending (Arith.), the operation of changing
        numbers of a lower into others of a higher denomination,
        as cents to dollars.
     Reduction descending (Arith.), the operation of changing
        numbers of a higher into others of a lower denomination,
        as dollars to cents.
        [1913 Webster]
     Syn: Diminution; decrease; abatement; curtailment;
          subjugation; conquest; subjection.
          [1913 Webster]

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