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Real Numbers Course

Real Numbers Course
4 to 360 hours of 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 Differentials

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 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

Your classes are perfect. I purchased the one-year package and finally have the chance to follow several topics I'm interested in without having to switch platforms... thank you for everything you do, I've already recommended you to others...
Giulio Carlo
Giulio CarloDigital Marketing Student
I like how the lessons get straight to the point and how I can switch chapters and skip content I don't need.
Mariana Ferres
Mariana FerresPhotography Student
I like the content and the way the videos are presented and transcribed, which speeds up the process!
Luciana Alvarenga
Luciana AlvarengaNail Design Student
The platform is fast and easy to use. The variety of content and the supplementary videos really help with learning.
Giulio Carlo
Giulio CarloPrompt Engineering Student

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