## Lectures on Fundamental Concepts of Algebra and Geometry |

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addition and multiplication axioms bounding sphere called cardinal number characterize circle class of points commutative complex numbers conception concrete representation congruent consider consistent defined definition denumerable discrete sequence discussion E. H. Moore elementary equal equation equivalent Euclid's Euclid's Elements euclidean geometry example fact fifth postulate finite follows formal logical four-dimensional fractions function fundamental geometric interpretation given infinite number intervals irrational numbers last element limit linear linear order m-class containing mathe mathematical science means method metric geometry negative numbers non-euclidean geometry notion number of elements number system obtained one-to-one correspondence parallel parallel postulate point of view positive integers positive number problem projective geometry proof properties pupil quaternions question rational numbers readily seen real numbers regarded relation represented satisfied segment set of assumptions shortest lines space sphere square straight line Suppose symbol term mathematical theorem tion triangle types of order undefined terms variable zero