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

from 4 to 360h flexible workload
certificate valid 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 concise proofs for projects and advanced maths.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers with sharp, quick reasoning.
- Handle rational numbers precisely: equivalence, closure, and solid proofs.
- Demonstrate irrationality of √2, π, and e using clear proof outlines.
- Prove density of rationals and reals, constructing examples between any reals.
- Craft concise, refined proofs and expository pieces for mathematical 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.What our students say
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