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

4 to 360 hours 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 ordering on the real line, operations on rationals and irrationals, and develop skills in crafting concise proofs for projects and advanced maths.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers using sharp, efficient reasoning.
- Handle rational numbers with rigour: equivalence, closure properties, and solid proofs.
- Clearly outline proofs of irrationality for √2, π, and e.
- Demonstrate density of rationals and reals, constructing examples between any reals.
- Craft concise, professional mathematical proofs and explanatory 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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