Real Numbers Course
Gain deep insights into real numbers, spanning rationals to irrationals such as √2, π, and e. Master proofs of density on the real line, operations, and polished 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 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 precise reasoning.
- Rigorous manipulation of rational numbers: equivalence, closure, proofs.
- Explain irrationality of √2, π, and e with clear proof outlines.
- Prove density of rationals and reals, construct numbers between reals.
- Craft concise, professional mathematical proofs and expositions.
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
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
Eu gosto de como as lições são direto ao ponto e como eu consigo alterar capítulos e pular conteúdos que não preciso.

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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