Real Numbers Course
Gain a deep understanding of real numbers, progressing from 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 advanced mathematics.

4 to 360 hours of flexible workload
certificate valid in your country
What Will I Learn?
This course provides a strong foundation in number systems, covering natural numbers, rationals, irrationals, and constants like √2, π, and e. Learners will study 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 accurately and swiftly.
- Handle rational numbers with rigour, including equivalence, closure, and proofs.
- Demonstrate irrationality of √2, π, and e using succinct proof outlines.
- Establish density of rationals and reals, constructing examples between any reals.
- Produce concise, refined proofs and expository pieces for mathematical 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
FAQs
Who is Elevify? How does it work?
Do the courses come with a certificate?
Are the courses free?
What is the course duration?
What are the courses like?
How do the courses work?
What is the duration of the courses?
What is the cost or price of the courses?
What is an online course and how does it work?
PDF Course