• Corpus ID: 15234800

CAUCHY’S CONSTRUCTION OF R

@inproceedings{Kemp2016CAUCHYSCO,
  title={CAUCHY’S CONSTRUCTION OF R},
  author={Todd Kemp},
  year={2016}
}
π = 3.14159 . . . to mean that π is a real number which, accurate to 5 decimal places, equals the above string. To be precise, this means that |π − 3.14159| < 10−5. But this does not tell us what π is. If we want a more accurate approximation, we can calculate one; to 10 decimal places, we have π = 3.1415926536 . . . Continuing, we will develop a sequence of rational approximations to π. One such sequence is 3, 3.1, 3.14, 3.142, 3.1416, 3.14159, . . . But this is not the only sequence of… 
Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties

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