Real Numbers Course
Gain deep insights 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 reasoning and communication skills 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. Learners explore density and ordering on the real line, operations on rationals and irrationals, and develop skills in crafting concise proofs for projects and advanced studies.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers using quick, accurate logic.
- Handle rational numbers with rigor, including equivalence, closure, and proofs.
- Demonstrate irrationality of √2, π, and e through succinct proof outlines.
- Establish density of rationals and reals, constructing examples between any reals.
- Produce concise, refined proofs and expository work 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 workload.What our students say
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