Real Numbers Course
Build a strong foundation in real numbers, covering rationals to irrationals like √2, π, and e. Master proofs, density properties on the real line, and clear mathematical writing to boost your reasoning and expression skills for advanced maths studies.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course builds a firm, hands-on understanding of number systems, spanning natural numbers, rationals, irrationals, and essentials like √2, π, and e. Dive into density and ordering on the real line, operations on rationals and irrationals, and hone skills in crisp proofs and explanations for compact projects and higher-level maths.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers with sharp, quick reasoning.
- Handle rational numbers precisely: equivalence, closure, and solid proofs.
- Outline proofs of irrationality for √2, π, and e clearly and briefly.
- Prove density of rationals and reals, building numbers between any two.
- Craft concise, refined proofs and math projects for deeper 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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