Basic Concepts of Mathematics |
Common terms and phrases
A₁ absolute values additive inverse angle Archimedean field Archimedean property assume basic unit vectors called closure law complete field complete ordered field complex numbers consists contains coordinates Corollary countable defined definition denoted direction cosines disjoint domain dot products E-classes edgelengths equal equation equivalence relation exactly example field F Find finite formula geometric given Hence Hint holds hyperplane implies induction inequalities integers intersection interval isomorphism laws lim xn line segment linear space lower bound mapping f means multiplication n-tuple natural elements natural numbers norm notation Note obtain one-to-one ordered field ordered pairs perpendicular plane points Problem Prove the following q-ary real numbers replaced right-bounded satisfy scalar Similarly subset supA supremum symbols triangle inequality trichotomic unique upper bound vector space Verify write
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Page 2 - elements of a set A are also elements of a set B, we say that A is a subset of B, and write A c B. In
Page 133 - E Eż can be expressed, in a unique way, as a linear combination of the n basic unit vectors
Page 4 - (c) The difference A — B is the set of all elements that are in A but not in B
Page 177 - multiply the numerator and the denominator by the conjugate of the denominator to
Page 165 - the points a and b are called the endpoints of the interval.
Page 151 - between a point on one line and a point on the other line.
Page 135 - is said to be linearly dependent if there are scalars a 1 , a 2