Real Numbers Course
Build a deep understanding of real numbers, including rationals and irrationals such as √2, π, and e. Delve into proofs of density on the real line, operations, and mathematical writing to enhance reasoning and communication skills for advanced mathematics coursework.

4 to 360h flexible workload
certificate valid in your country
What will I learn?
This course provides 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 develop skills in crafting concise proofs for projects and advanced math studies.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers using precise reasoning.
- Rigorous manipulation of rational numbers: equivalence, closure, and proofs.
- Explain irrationality of √2, π, and e with clear proof outlines.
- Prove density of rationals and reals, constructing examples between numbers.
- Craft concise, polished proofs and expository math projects.
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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