Real Numbers Course
Gain deep insights into real numbers, progressing from rationals to irrationals such as √2, π, and e. Master 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 real 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 reasoning.
- Handle rational numbers with rigour: equivalence, closure properties, and 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.
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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