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This paper looks at how ancient mathematicians (and especially thePythagorean school) were faced by problems/paradoxes associated with theinfinite which led them to juggle two systems of numbers: the discretewhole/rationals which were handled arithmetically and the continuous magnitudequantities which were handled geometrically. We look at how approximations andmixed numbers (whole numbers with fractions) helped develop the arithmetizationof geometry and the development of mathematical analysis and real numbers.

The paradoxes and the infinite dazzled ancient mathematics and continue to do so today