Real Numbers Course
Gain deep insight into real numbers, from rationals to irrationals such as √2, π, and e. Master proofs of density on the real line, operations, and polished mathematical writing to enhance reasoning and communication 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 real numbers, covering natural numbers, rationals, irrationals like √2, π, and e. Learners study density and order on the real line, operations on rationals and irrationals, and develop skills in concise proofs for projects and advanced math studies.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers quickly and accurately.
- Handle rational numbers with rigor, including equivalence, closure, and proofs.
- Demonstrate irrationality of √2, π, and e using clear proof outlines.
- Prove density of rationals in reals and construct numbers between any two reals.
- Craft concise, professional proofs and math exposition for analysis studies.
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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