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Real Numbers Course

Real Numbers Course
from 4 to 360h flexible workload
valid certificate in your country

What will I learn?

The Real Numbers Course gives you a solid, practical grasp of number systems, from natural and rational values to irrationals and key constants like √2, π, and e. You will explore density and order on the real line, see how operations affect rational and irrational values, and practice writing clear, concise proofs and explanations suitable for short, well-structured projects and further advanced study.

Elevify advantages

Develop skills

  • Classify real, rational, and irrational numbers with precise, fast reasoning.
  • Manipulate rational numbers rigorously: equivalence classes, closure, and proofs.
  • Explain √2, π, and e irrationality with clear, concise proof sketches.
  • Prove density results on ℚ and ℝ and construct rationals or irrationals between reals.
  • Write short, polished mathematical proofs and expository projects for analysis.

Suggested summary

Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.
Workload: between 4 and 360 hours

What our students say

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