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if 0 ≤ a and 0 ≤ b, then 0 ≤ ab. Because ≤ is a total order , for any number a , either 0 ≤ a or a ≤ 0 (in which case the first property above implies that 0 ≤ − a ). In either case 0 ≤ a 2 ; this means that i 2 > 0 and 1 2 > 0 ; so −1 > 0 and 1 > 0 , which means (−1 + 1) > 0; contradiction.
≤ 1. Means "less than or equal to". That is, whatever A and B are, A ≤ B is equivalent to A < B or A = B. 2. Between two groups, may mean that the first one is a subgroup of the second one. ≥ 1. Means "greater than or equal to". That is, whatever A and B are, A ≥ B is equivalent to A > B or A = B. 2.
≤ may refer to: Inequality (mathematics) , relation between values; a ≤ b means " a is less than or equal to b " Subgroup , a subset of a given group in group theory; H ≤ G is read as " H is a subgroup of G "
In mathematics, particularly in order theory, an upper bound or majorant [1] of a subset S of some preordered set (K, ≤) is an element of K that is greater than or equal to every element of S. [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.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
The positive integers may be partially ordered by divisibility: if a divides b (that is, if b is an integer multiple of a) write a ≤ b (or equivalently, b ≥ a). (Note that the usual magnitude-based definition of ≤ is not used here.) Under this ordering, the positive integers become a lattice, with meet given by the gcd and join given by ...
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