Real Numbers Course
Deepen your understanding of real numbers, from rationals to irrationals like √2, π, and e. Explore proofs, density on the real line, and clear mathematical writing to strengthen your reasoning and communication in advanced mathematics.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
The Real Numbers Course gives you a solid, practical grasp of number systems, from natural and rational values to irrationals and key constants like √2, π, and e. You will explore density and order on the real line, see how operations affect rational and irrational values, and practice writing clear, concise proofs and explanations suitable for short, well-structured projects and further advanced study.
Elevify advantages
Develop skills
- Classify real, rational, and irrational numbers with precise, fast reasoning.
- Manipulate rational numbers rigorously: equivalence classes, closure, and proofs.
- Explain √2, π, and e irrationality with clear, concise proof sketches.
- Prove density results on ℚ and ℝ and construct rationals or irrationals between reals.
- Write short, polished mathematical proofs and expository projects for 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 workload.What our students say
As suas aulas são perfeitas. Adquiri o pacote de um ano e, finalmente, tenho a oportunidade de acompanhar diversos temas do meu interesse sem precisar mudar de plataforma... agradeço por tudo o que fazem, já recomendei vocês a outras pessoas...

Giulio CarloAluno de Marketing Digital
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Mariana FerresAluna de Fotografia
Gosto do conteúdo e do modo de apresentação e transcrição de vídeos, o que acelera o processo!

Luciana AlvarengaAluna de Design de Unhas
A plataforma é rápida, simples de usar. A diversidade de conteúdo e os vídeos complementares ajudam muito no aprendizado.

Giulio CarloAluno de Engenharia de Prompt
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