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jk-terminology - Oft-used notation of Prof JLF King...

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Oft-used notation of Prof. JLF King Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA [email protected] Webpage http://www.math.ufl.edu/ squash/ 23 April, 2011 (at 22:51 ) Names for sets of numbers An expression such as k N ( read as “ k is an element of N ” or “ k in N ) means that k is a natural number; a natnum . N = natural numbers = { 0 , 1 , 2 , . . . } . Z = integers = { . . . , - 2 , - 1 , 0 , 1 , . . . } . For the set { 1 , 2 , 3 , . . . } of positive integers, the posints , use Z + . Use Z - for the negative integers, the negints . Q = rational numbers = { p q | p Z and q Z + } . Use Q + for the positive ratnums and Q - for the negative ratnums. R = reals. The posreals R + and the negreals R - . C = complex numbers, also called the complexes . Phrases used in proofs WLOG : ‘ Without loss of generality ’. TFAE : ‘ The follow- ing are equivalent ’. OTForm : ‘ of the form ’. FTSOC : For the sake of contradiction ’. Use iff : ‘ if and only if ’. IST : ‘ It Suffices to ’ as in ISTShow , ISTExhibit . Use w.r.t : ‘ with respect to ’ and s.t : ‘ such that ’. Latin: e.g : exempli gratia , ‘ for example ’. i.e : id est , ‘ that is ’. Names for Mathematical Objects Poly(s) : ‘ polynomial(s) ’. Irred : ‘ irreducible ’. Coeff : coefficient ’ and var(s) : variable(s) ’ and parm(s) : parameter(s) ’. Expr. : expression ’. Fnc : function ’ (so ratfnc : means rational function , a ratio of polynomials). Seq : ‘ sequence ’. Soln : solution ’. Prop’n : proposition ’. CEX : Counterexample ’. Eqn : ‘ equation ’. RhS: ‘ RightHand Side ’ of an eqn or inequality. LhS: lefthand side ’. Sqrt : square-root ’, e.g, “the sqrt of 16 is 4”. Cts : continuous ’ and cty : ‘ continuity ’. Ptn : ‘ partition ’, but pt : ‘ point ’, as in “a fixed-pt of a map”. Prefixes: Use nv- for ‘ non-void ’, e.g “the cartesian product of two nv-sets is non-void”. Use nt- for ‘ non- trivial ’, e.g “the ( positive ) nt-divisors of 14 are 2 , 7 , 14, whereas the
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