Real Numbers Course
Gain deep insight into real numbers, spanning 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 higher 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 will study density and order on the real line, operations on rationals and irrationals, and develop skills in crafting precise proofs and explanations for projects and advanced studies.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers using sharp, quick reasoning.
- Handle rational numbers with rigour: equivalence, closure, and solid proofs.
- Clearly outline proofs of irrationality for √2, π, and e.
- Demonstrate density in rationals and reals, constructing examples between any reals.
- Craft concise, refined proofs and expository pieces 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 workloadWhat our students say
Your classes are perfect. I got the one-year package and finally have the chance to follow several topics I'm interested in without having to switch platforms... thank you for everything you do, I've already recommended you to others...

Giulio CarloDigital Marketing Student
I like how the lessons get straight to the point and how I can switch chapters and skip content I don't need.

Mariana FerresPhotography Student
I like the content and the way the videos are presented and transcribed, which speeds up the process!

Luciana AlvarengaNail Design Student
The platform is fast and easy to use. The variety of content and the extra videos really help with learning.

Giulio CarloPrompt Engineering Student
FAQ
Who is Elevify? How does it work?
Do the courses have certificates?
Are the courses free?
What is the course workload?
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 EAD or online course and how does it work?
PDF Course