Transcription of Commonly Used Mathematical Notation - Columbia …
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Commonly Used Mathematical Notation - Columbia …
Commonly Used MathematicalNotation1 Logical StatementsCommon symbols for logical statement:_logical disjunction:"or"Note:in mathematics this is always an "inclusive or" "onorthe otheror both"^logical conjunction:"and":logical negation:"not"!material implication:implies; if .. thenNote:P!Qmeans:ifPis true thenQis also true;ifPis false then nothing is said aboutQcan also be expressed as:ifPthenQPimpliesQQ, ifPPonly ifQPis a su cient condition forQQis a necessary condition forPsometimes writen as)f:X!Yfunction arrow:functionfmaps the setXinto the setY function composition:f gfunction such that(f g)(x) =f(g(x))$material equivalence:if and only if (i )1 Note:P$Qmeans:meansPis true ifQis true andPis false ifQis falsecan also be expressed as:P;if and only ifQQ, if and only ifPPis a necessary and su cient condition forQQis a necessary and su cient condition forPsometimes writen as, is much less than is much greater than)therefore8universal quanti cation:for all/any/each9existential quanti cation:there exists9!
2 Set Notation A set is some collection of objects. The objects contained in a set are known as elements or members. This can be anything from numbers, people, other sets, ... Commonly used operations on sets: [ Union A[B set containing all elements of A and B. A[B = fx j x 2 A_x 2 Bg \ Intersect A\B set containing all those elements that A and ...
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