Inaequatio Notae | Tabula navigationis"De limitis aequationum,"

Mathematica


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Inaequatio[1] est sententia mathematica quae dicit quantitatem aliquem maiorem vel minorem esse alia quantitate. Sunt quattuor symbola inaequalitatis: < (est minor quam), ≤ (vel minor est, vel aequat), > (est maior quam), ≥ (vel maior est, vel aequat). Hoc modo utenda:


  1. 5 < 7 verum est, quod quinque quantitas minor est quam septem

  2. 5 ≤ 7 quoque verum est, et 5 ≤ 5, sed non 5 ≤ 4

  3. 7 > 5 idem significat quod 5 < 7

  4. et 7 ≥ 5 idem significat quod 5 ≤ 7

Si inaequatio quantitates variables continet, possumus eam solvere sicut aequationes solvimus. Sed, si inequatio multiplicatur per quantitatem negativam, signum inaequationis ipsius contrarium fiat. Exempli gratia:


Verum est 5 < 7. Multiplica ambo latera per –1: nunc –5 > –7 (signo contrario).

Haec sunt exempla inaequationum solvendarum:


  • 5 + x < 7. Subtrahe: x < 7 – 5 = 2

  • 3 – x ≥ 12 Subtrahe: -x ≥ 9 Multiplica: x ≤ 9



Inequatio y ≤ x + 2 regionem colore roseam determinat.


Aequatio gradus primi inter duas variabiles lineam determinat. Inaequatio autem dimidiam partem plani determinat. Exempli gratia, si y ≤ x + 2, valores (0, 0) et (0, 1) et (0, 2) inaequationem validam faciunt (quod 0 ≤ 0 + 2, 1 ≤ 0 + 2, 2 ≤ 0 + 2). Omnes pars plani in qua sunt hae puncta est solutio. Si inaequatio signis "≤" vel "≥" utitur, linea ipsa est pars solutionis; si "<" vel ">" signis, linea non est pars solutionis.



Notae |



  1. ↑ Hoc nomine utitur Dominicus Pianus (1839), "De limitis aequationum," Novi Commentarii Academiae Scientiarum Instituti Bononiensis, 3:237–250; verbum pp. 240 et 242 invenitur.









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