Real Numbers Course
Gain 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 effective mathematical writing to enhance reasoning and communication skills for higher 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. Learners will study density and order on the real line, operations on rationals and irrationals, and develop skills in crafting precise proofs and explanations for projects and advanced studies.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers using sharp, quick reasoning.
- Handle rational numbers with rigour: equivalence, closure, and solid proofs.
- Clearly outline proofs of irrationality for √2, π, and e.
- Demonstrate density in 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 workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workloadWhat our students say
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