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[2] [3] Dually, a lower bound or minorant of S is defined to be an element of K that is less than or equal to every element of S. A set with an upper (respectively, lower) bound is said to be bounded from above or majorized [ 1 ] (respectively bounded from below or minorized ) by that bound.
A real-valued function is bounded if and only if it is bounded from above and below. [ 1 ] [ additional citation(s) needed ] An important special case is a bounded sequence , where X {\displaystyle X} is taken to be the set N {\displaystyle \mathbb {N} } of natural numbers .
A subset S of a partially ordered set P is called bounded above if there is an element k in P such that k ≥ s for all s in S. The element k is called an upper bound of S. The concepts of bounded below and lower bound are defined similarly. (See also upper and lower bounds.)
A geophyte (earth+plant) is a plant with an underground storage organ including true bulbs, corms, tubers, tuberous roots, enlarged hypocotyls, and rhizomes. Most plants with underground stems are geophytes but not all plants that are geophytes have underground stems. Geophytes are often physiologically active even when they lack leaves.
Hypogeal germination (from Ancient Greek ὑπόγειος [hupógeios] 'below ground', from ὑπό [hupó] 'below' and γῆ [gê] 'earth, ground') is a botanical term indicating that the germination of a plant takes place below the ground. An example of a plant with hypogeal germination is the pea (Pisum sativum). The opposite of hypogeal is ...
The theorem states that if you have an infinite matrix of non-negative real numbers , such that the rows are weakly increasing and each is bounded , where the bounds are summable < then, for each column, the non decreasing column sums , are bounded hence convergent, and the limit of the column sums is equal to the sum of the "limit column ...
In biology, the canopy is the aboveground portion of a plant cropping or crop, formed by the collection of individual plant crowns. [ 1 ] [ 2 ] [ 3 ] In forest ecology , the canopy is the upper layer or habitat zone, formed by mature tree crowns and including other biological organisms ( epiphytes , lianas , arboreal animals , etc.). [ 4 ]
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