Real Numbers Course
Gain deep insight into real numbers, from rationals to irrationals such as √2, π, and e. Master proofs, density properties on the real line, and clear mathematical writing to boost your reasoning skills and communication for higher-level mathematics studies.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course builds a strong foundation in number systems, covering natural numbers, rationals, irrationals, and constants like √2, π, and e. You'll study density and order on the real line, operations on rationals and irrationals, and learn to craft precise proofs and explanations for projects and advanced maths.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers quickly and accurately.
- Handle rational numbers with rigour: equivalence, closure, and solid proofs.
- Demonstrate irrationality of √2, π, and e using neat proof outlines.
- Prove density in rationals and reals, constructing examples between any two reals.
- Produce concise, professional maths proofs and project write-ups 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.What our students say
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