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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. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds. [4]
The metric space (M, d) is a bounded metric space (or d is a bounded metric) if M is bounded as a subset of itself. Total boundedness implies boundedness. For subsets of R n the two are equivalent. A metric space is compact if and only if it is complete and totally bounded. A subset of Euclidean space R n is compact if and only if it is closed and
Structural bench – Long, relatively narrow land bounded by distinctly steeper slopes above and below; Structural terrace – A step-like landform; Tepui – Table-top mountain or mesa in the Guiana Highlands of South America; Tessellated pavement – Relatively flat rock surface that is subdivided into more or less regular shapes by fractures
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 .
Epigean – occurring on the ground. Epigeic – plants with stolons on the ground. Epigeous – on the ground. Used for leaf fungus that live on the surface of the leaf. Epiphloedal – growing on the bark of trees. Epiphloedic – an organism that grows on the bark of trees. Epiphyllous – growing on the leaves.
In particular, every subset Y of X is bounded above by X and below by the empty set ∅ because ∅ ⊆ Y ⊆ X. Hence, it is possible (and sometimes useful) to consider superior and inferior limits of sequences in ℘(X) (i.e., sequences of subsets of X). There are two common ways to define the limit of sequences of sets. In both cases:
Besides the superposition of different plants growing on the same soil, there is a lateral impact of the higher layers on adjacent plant communities, for example, at the edges of forests and bushes. This particular vegetation structure results in the growth of certain vegetation types such as forest mantle and margin communities. [citation needed]
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 ...