termwiseadv.adj.
/ˈtəːmwʌɪz/, U.S. /ˈtərmˌwaɪz/ Mathematics.
A. adv.† 1. So as to form the denominator and numerator of a fraction. Cf. term n. 14a(a). Obsolete. rare.
ΚΠ
1868 A. Sandeman Pelicotetics Pref. p. vii The fraction symbol..is sometimes found..with symbols written termwise of two magnitudes neither expressed numerically.
2. With reference to an operation on a mathematical sequence or algebraic expression: term by term (see 14b(a), term n. 14c).
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > [adverb] > treating each term separately
termwise1912
1912 J. Pierpont Lect. Theory Functions Real Variables II. v. 180 In this case we can obviously integrate termwise, although the convergence is not uniform.
1979 Proc. London Math. Soc. 38 390 We then integrate termwise.
2014 M. Overholt Course in Analytic Number Theory iv. 148 The integral..is calculated trivially by multiplying out the integrand..and integrating termwise.
B. adj.
Designating a mathematical operation performed term by term (see term n. 14c, 14b(a)).
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets > of sequences > series
intermediate1648
converging1728
convergent1816
zeroth1850
tactical1864
oscillatory1893
termwise1903
sociable1964
1903 Bull. Amer. Math. Soc. 9 502 In such books we find a systematic application of the algorithm of inequalities to such questions as..term-wise differentiation and integration of series.
1930 T. Fort Infinite Series vii. 74 Termwise multiplication of series.
1979 Adv. in Appl. Probability 11 221 This fact will henceforth justify all termwise operations on sums of the Pt(γ,n) such as termwise integration, differentiation, etc.
2012 Ann. Statistics 40 3167 The termwise multiplication of these additional columns results in a vector of 1.
This entry has been updated (OED Third Edition, March 2017; most recently modified version published online March 2022).
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adv.adj.1868