MTH 141 Lecture Notes - Lecture 1: Empty Set

• School: University of Rochester
• Department: Mathematics
• Course: MTH 141
• Professor: naomi

Document Summary

Interval notation ex) (cid:867)(cid:870)(cid:1540)x(cid:1540)(cid:867)(cid:873) (cid:878) [(cid:867)(cid:870),(cid:867)(cid:873)] (cid:866)(cid:871)(cid:877)x(cid:1540)(cid:867)(cid:866)(cid:878) (cid:857)(cid:866)(cid:871),(cid:867)(cid:866)] Endpoints of intervals: if an endpoint is included, then use [ or ]. For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7]. I(cid:927)(cid:919)i(cid:927)i(cid:933)(cid:918) i(cid:927)(cid:933)(cid:918)(cid:931)(cid:935)al(cid:932)(cid:875) f(cid:928)(cid:931) i(cid:927)(cid:919)i(cid:927)i(cid:933)(cid:918) i(cid:927)(cid:933)(cid:918)(cid:931)(cid:935)al(cid:932), (cid:934)(cid:932)(cid:918) i(cid:927)(cid:919) (cid:919)(cid:928)(cid:931) (infinity) or -inf for - (cid:857)-infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed [6,inf). Unions of intervals: if the set includes more than one interval, they are joined using the union symbol u. For example, the set consisting of all points in (-3,7] together with all points in [-8,-5) is expressed [-8,-5)u(-3,7]. All sets should be expressed in their simplest interval notation form, with no overlapping intervals. Empty intervals: if the answer is the empty set, you can specify that by using braces with nothing inside: { } Special symbols: you can use r as a shorthand for all real numbers.