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765:, which are free variables for which values are sought that cause the condition to be fulfilled. To be precise, what is sought are often not necessarily actual values, but, more in general, expressions. A
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can be read as "and"); the set of its solutions is shown in blue in the picture (the red, green, and orange line corresponding to the 1st, 2nd, and 3rd conjunct, respectively). For a larger example. see
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means finding what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an inequation or a conjunction of several inequations. These expressions contain one or more
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In some cases, the term "inequation" can be considered synonymous to the term "inequality", while in other cases, an inequation is reserved only for statements whose inequality relation is "
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that satisfies the inequation(s); in other words, expressions such that, when they are substituted for the unknowns, make the inequations true propositions. Often, an additional
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Usually because of the properties of certain functions (like square roots), some inequations are equivalent to a combination of multiple others. For example, the inequation
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denoting the values in question, with a relational sign between them indicating the specific inequality relation. Some examples of inequations are:
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III also supports solving algorithms for particular classes of inequalities (and other relations) as a basic language feature. For more, see
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918:{\displaystyle 0\leq x_{1}\leq 690-1.5\cdot x_{2}\;\land \;0\leq x_{2}\leq 530-x_{1}\;\land \;x_{1}\leq 640-0.75\cdot x_{2}}
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of several inequations involving common expressions, by chaining them together. For example, the chain
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In rare cases, chains without such implications about distant terms are used. For example
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holds between two values. It is usually written in the form of a pair of
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finds optimal solutions of linear inequations. The programming language
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is logically equivalent to the following three inequations combined:
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is a conjunction of inequations, partly written as chains (where
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of the inequation is an assignment of expressions to the
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Computer support in solving inequations is described in
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Mathematical statement that two values are not equal
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1023:{\displaystyle \textstyle {\sqrt {f(x)}}<g(x)}
567:{\displaystyle i\neq 0~~\mathrm {and} ~~0\neq j}
686:{\displaystyle a<b~~\mathrm {and} ~~b>c}
1159:{\displaystyle f(x)<\left(g(x)\right)^{2}}
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285:A shorthand notation is used for the
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1220:. John Wiley and Sons. p. 252.
693:, which does not imply any order of
58:adding citations to reliable sources
1362:"Optimization - The simplex method"
1338:"Linear Programming: Introduction"
1300:Introduction to Lattices and Order
749:) for a sample list of inequations
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323:{\displaystyle 0\leq a<b\leq 1}
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509:{\displaystyle i\neq 0\neq j}
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745:Solution set (portrayed as
628:{\displaystyle a<b>c}
209:{\displaystyle x+y+z\leq 1}
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1061:{\displaystyle f(x)\geq 0}
951:Linear programming#Example
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1097:{\displaystyle g(x)>0}
1397:Mathematical terminology
1307:in exercise 1.11, p.23.
1192:Inequality (mathematics)
976:Combinations of meanings
596:{\displaystyle i\neq j.}
429:which also implies that
1366:Encyclopedia Britannica
574:, which does not imply
263:{\displaystyle x\neq 0}
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737:Solving inequations
1392:Elementary algebra
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65:Find sources:
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43:This article
41:
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32:
31:
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22:
1369:. Retrieved
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1356:
1345:. Retrieved
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1277:. Retrieved
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1249:
1246:"Inequation"
1217:
1211:
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955:
927:
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275:not equal to
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69:"Inequation"
64:
52:Please help
47:verification
44:
1270:"BestMaths"
1187:Equals sign
753:Similar to
603:Similarly,
287:conjunction
146:expressions
134:mathematics
1386:Categories
1371:2019-12-03
1347:2019-12-03
1342:Purplemath
1279:2019-12-03
1255:2019-12-03
1203:References
781:solution.
142:inequality
138:inequation
110:March 2010
80:newspapers
1053:≥
936:∧
903:⋅
897:−
891:≤
877:∧
863:−
857:≤
844:≤
837:∧
823:⋅
817:−
811:≤
798:≤
775:objective
585:≠
559:≠
527:≠
501:≠
495:≠
411:≤
347:≤
315:≤
303:≤
255:≠
201:≤
1323:89009753
1297:(1990).
1182:Equation
1170:See also
771:unknowns
767:solution
763:unknowns
779:optimal
277:" (≠).
94:scholar
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966:Prolog
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