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In an inequality, the less-than sign and greater-than sign always "point" to the smaller number. Put another way, the "jaws" (the wider section of the symbol) always direct to the larger number. The less-than-sign is sometimes used to represent a total order , partial order or preorder .
1.435 m – standard gauge of railway track used by about 60% of railways in the world = 4 ft 8 1 ⁄ 2 in; 2.5 m – distance from the floor to the ceiling in an average residential house [119] 2.7 m – length of the Starr Bumble Bee II, the smallest plane; 2.77–3.44 m – wavelength of the broadcast radio FM band 87–108 MHz
So are 1 and 2, 1 and 9, or 1 and 0.2. However, 1 and 15 are not within an order of magnitude, since their ratio is 15/1 = 15 > 10. The reciprocal ratio, 1/15, is less than 0.1, so the same result is obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in "decades" (i.e., factors of ten). [2]
The second comparison is between x 2 and y 2, and so on. For example, the vector (3,5,3) is lexicographically smaller than (4,2,4), since the first element in the former is 3 and in the latter it is 4. Similarly, (4,2,4) is lexicographically larger than (2,4,4). The following algorithm can be used to compute whether x is leximin-larger than y:
However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
Goldbach's weak conjecture, every odd number greater than 5 can be expressed as the sum of three primes, is a consequence of Goldbach's conjecture. Ivan Vinogradov proved it for large enough n (Vinogradov's theorem) in 1937, [1] and Harald Helfgott extended this to a full proof of Goldbach's weak conjecture in 2013. [2] [3] [4]
For example, 5 is a lower bound for the set S = {5, 8, 42, 34, 13934} (as a subset of the integers or of the real numbers, etc.), and so is 4. On the other hand, 6 is not a lower bound for S since it is not smaller than every element in S. 13934 and other numbers x such that x ≥ 13934 would be an upper bound for S.
1. Strict inequality between two numbers; means and is read as "less than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2.