Search Result for "monotonically increasing function":
The Collaborative International Dictionary of English v.0.48:
Increase \In*crease"\, v. i. [imp. & p. p. Increased; p. pr. &
vb. n. Increasing.] [OE. incresen, encresen, enrescen, OF.
encreistre, fr. L. increscere; pref. in- in + crescere to
grow. See Crescent, and cf. Decrease.]
1. To become greater or more in size, quantity, number,
degree, value, intensity, power, authority, reputation,
wealth; to grow; to augment; to advance; -- opposed to
The waters increased and bare up the ark. --Gen.
He must increase, but I must decrease. --John iii.
The heavens forbid
But that our loves and comforts should increase,
Even as our days do grow! --Shak.
2. To multiply by the production of young; to be fertile,
fruitful, or prolific.
Fishes are more numerous or increasing than beasts
or birds, as appears by their numerous spawn. --Sir
3. (Astron.) To become more nearly full; to show more of the
surface; to wax; as, the moon increases.
Increasing function (Math.), a function whose value
increases when that of the variable increases, and
decreases when the latter is diminished; also called a
monotonically increasing function.
Syn: To enlarge; extend; multiply; expand; develop; heighten;
amplify; raise; enhance; spread; aggravate; magnify;
Usage: To Increase, Enlarge, Extend. Enlarge implies to
make larger or broader in size. Extend marks the
progress of enlargement so as to have wider
boundaries. Increase denotes enlargement by growth and
internal vitality, as in the case of plants. A kingdom
is enlarged by the addition of new territories; the
mind is enlarged by knowledge. A kingdom is extended
when its boundaries are carried to a greater distance
from the center. A man's riches, honors, knowledge,
etc., are increased by accessions which are made from
time to time.