Real Numbers Course
Gain deep insights into real numbers, spanning rationals to irrationals such as √2, π, and e. Master proofs, density properties on the real line, and effective 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 precise proofs and explanations for projects and advanced studies.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers using quick, accurate logic.
- Handle rational numbers with rigour: equivalence, closure, and solid 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 the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
Your lessons are perfect. I purchased the one-year package and finally have the opportunity to follow various topics of interest without needing to change platforms... I thank you for everything you do, I've already recommended you to other people...

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

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

Luciana AlvarengaNail Design Student
The platform is fast, simple to use. The diversity of content and complementary videos really help with learning.

André FelipePrompt Engineering Student
FAQ
Who is Elevify? How does it work?
Do the courses have certificates?
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 EAD or online course and how does it work?
PDF Course