The Natural Integers

Become an efficient calculator, from basics practice to deeply understood theory

The aim of that course is to give you the mastery of the construction and manipulation of the natural integers, the numbers we count with.

Starting with practical animated graphics, and Python manipulations, you will become by the end of that course a master in:

  • Counting and constructing the natural integers set, from zero to infinity
  • Comparing natural integers, and ordering the natural integers set
  • Adding, subtracting and multiplying the natural integers, including doing all these operations in a unique formula.
  • Understanding the powers of 10 and the exponential notation
  • Exponentiating the natural integers, and manipulating polynomials
  • Comparing the results of additions and/or subtraction
  • Comparing the results of multiplications and/or exponentiation

At the top of all that, you will master the powerful proof by recursion, a tremendously useful method of proving theorems, based on the natural integers set construction.

That course includes 39 high quality video lectures, plus 9 downloadable recapitulative documents, one per section, with all the proofs.


Your Instructor


Fabienne Chaplais
Fabienne Chaplais

Fabienne holds the “Agrégation de Mathématiques“
, the French Highest Degree to teach math in Secondary Schools.

After a career of 26 years as a R&D engineer in applied mathematics, she founded Mathedu (Re-engineering Mathematics) with her husband and collaborator François, 
to teach mathematics from a practical point of view, based on Python coding.

She is both an expert in teaching math and a passionated woman and will help you to experiment the joy of increasing your mastery in mathematics.

Course Curriculum


  Section 1: Introduction
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  Construct and Compare the Natural Integers
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  Section 3: Add Natural Integers
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  Section 4 - Subtract Natural Integers
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  Section 5 - Multiply Natural Integers
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  Section 6 - Master computation in the natural integers
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  Section 7 - Powers of 10 and decimal numeration
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  Section 8 - Exponentiation in N
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  Section 9 - The ordered monoid (N,+,≤)
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  Section 10 - The ordered semi-ring (N,+,x,≤)
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  Section 11 - Final Assessment - The sum of the n first positive integers
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  Section 12 - Conclusion
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Frequently Asked Questions


When does the course start and finish?
The course starts now and never ends! It is a completely self-paced online course - you decide when you start and when you finish.
How long do I have access to the course?
How does lifetime access sound? After enrolling, you have unlimited access to this course for as long as you like - across any and all devices you own.
What if I am unhappy with the course?
We would never want you to be unhappy! If you are unsatisfied with your purchase, contact us in the first 30 days and we will give you a full refund.

Wish to earn the Certificate of Arythmetics Mastery?

Enroll and take the course, answer the tests and final exam…

…and it's done!

Get started now!