Topic

Real numbers

6 concepts and 60 practice problems on real numbers, part of Real analysis.

6concepts
60exercises
≈ 3 hof study approx.

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Concepts

  • Ordered field 10 exercisesAn ordered field is a field F with a total order < compatible with addition and with multiplication by positive elements.
  • Supremum and infimum 10 exercisesGiven a set S of real numbers, its supremum is the least of its upper bounds and its infimum is the greatest of its lower bounds.
  • Completeness axiom 10 exercisesThe property that sets mathbb R apart from mathbb Q: every nonempty set S of reals with an upper bound M has a supremum.
  • Archimedean property 10 exercisesThe property of mathbb R by which, however small a positive number x is, some multiple of it by a natural n∈mathbb N exceeds any…
  • Absolute value 10 exercisesThe absolute value |x| of a real number x is its distance from zero on the real line; |x-a| measures the distance between x and a.
  • Density of the rationals 10 exercisesProperty of the rationals mathbb Q inside the reals: between any two distinct reals a<b there is always a rational q.