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 precise mathematical writing to boost your reasoning skills and communication for higher-level mathematics.

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 dive into density and order on the real line, operations on rationals and irrationals, and craft clear proofs for projects and advanced math studies.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers with sharp, quick reasoning.
- Handle rational numbers precisely: equivalence, closure, and solid proofs.
- Clearly outline proofs for irrationality of √2, π, and e.
- Prove density of rationals and reals, constructing examples between any two reals.
- Craft concise, polished proofs and math 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.What our students say
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