SAMPLE College Math

‭It‬ ‭must‬ ‭be‬‭noted‬‭that‬‭in‬‭the‬‭above‬‭number‬‭line,‬‭there‬‭is‬‭a‬‭closed‬‭bracket‬‭[‬‭at‬‭2,‬‭which‬‭means‬‭that‬‭2‬‭is‬ ‭also‬‭included‬‭in‬‭the‬‭expression.‬‭In‬‭contrast,‬‭the‬‭expression‬ ‭is‬‭represented‬‭on‬‭the‬‭number‬ ‭ ‬ = {‭ ‬‭|‬‭ ‬ > ‭2‬} ‭line as follows:‬

‭When‬‭a‬‭parenthesis‬‭(‬‭is‬‭used‬‭on‬‭the‬‭number‬‭line,‬‭it‬‭means‬‭that‬‭all‬‭numbers‬‭greater‬‭than‬‭2,‬‭excluding‬‭2,‬ ‭are‬‭to‬‭be‬‭considered‬‭here.‬‭In‬‭other‬‭words,‬‭while‬‭using‬‭inequalities,‬‭we‬‭may‬‭make‬‭use‬‭of‬‭different‬‭types‬ ‭of‬ ‭brackets‬ ‭that‬ ‭have‬ ‭different‬ ‭meanings.‬ ‭For‬ ‭instance,‬ ‭means‬ ‭the‬ ‭set‬ ‭contains‬ ‭all‬‭the‬‭numbers‬ (‭ ‬, ‭ ‬) ‭between‬ ‭and‬ ‭,‬ ‭excluding‬ ‭and‬ ‭.‬ ‭On‬ ‭the‬ ‭contrary,‬ ‭means‬ ‭all‬ ‭numbers‬ ‭between‬ ‭and‬ ‭,‬ ‭ ‬ ‭ ‬ ‭ ‬ ‭ ‬ [‭ ‬, ‭‬‭ ‬] ‭ ‬ ‭ ‬ ‭including‬ ‭and‬ ‭.‬ ‭ ‬ ‭ ‬ ‭Similarly,‬ ‭means‬‭all‬‭numbers‬‭between‬ ‭and‬ ‭,‬‭inclusive‬‭of‬ ‭and‬‭exclusive‬‭of‬ ‭.‬‭This‬‭is‬‭known‬‭an‬ [‭ ‬, ‭‬‭ ‬) ‭ ‬ ‭ ‬ ‭ ‬ ‭ ‬ ‭interval notation. Let us understand this using a few examples:‬ ‭Set-Builder Notation‬ ‭Graphical Representation‬ ‭Interval Notation‬ {‭ ‬‭|‬‭‬‭ ‬‭‬ > ‭‬‭4‬} (‭4‬, ‭∞‬) {‭ ‬‭|‬‭‬‭ ‬‭‬ < ‭‬‭2‬} (− ‭∞‬, ‭2‬) { ‭ ‬‭| ‬‭ ‬‭ ‬‭ ‬‭≤ ‬‭ ‬‭1 ‬} (− ‭∞‬, ‭1‬] {‭ ‬‭|‬‭‬‭ ‬‭‬‭≥‬‭‬ − ‭3‬} [− ‭3‬, ‭∞‬) ‭C. Mathematical Translations of Equalities from Words‬ ‭An‬‭equation‬‭is‬‭used‬‭to‬‭show‬‭that‬‭two‬‭mathematical‬‭expressions‬‭are‬‭equal‬‭to‬‭each‬‭other.‬ ‭For‬‭instance,‬ ‭.‬ ‭This‬ ‭is‬ ‭as‬ ‭an‬ ‭equation‬ ‭since‬ ‭the‬‭expressions‬‭on‬‭both‬‭sides‬‭of‬‭the‬‭sentence‬‭are‬‭equal‬‭and‬ ‭2‬‭ ‬ + ‭5‬ = ‭9‬ ‭denoted by the equal to (=) sign. Some of the examples of equations are:‬ ‭3‬ + ‭5‬ = ‭8‬ ‭2 ‭5 ‭7 ‬ ‬‭ 0 * ‬‭– ‬‭ 1 ‭3 ‬ 0 ‬ = = ‬= ‭2 ‭8 8 ‭1 – 0 0 2 ‬ ‬ ‬ ‭In these examples, the expressions on either side of the equal sign are equal to each other.‬

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