Start Learning Numbers - Part 5 - Natural Numbers (Multiplication)

Thanks to all supporters! They are mentioned in the credits of the video :)

This is my video series about Start Learning Numbers. I hope that it will help everyone who wants to learn about the construction of numbers. This is something one needs as a good foundation for all advanced mathematics.

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#calculus
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I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[IgorVladK]

very nice series - looking forward to definition of real numbers!

[SuperCuteAnimeWaifu]

Blow my mind yet again. I know see why associativity holds up in this number field but breaks down in dot products of curls.

[johnroberts]

I am going to watch this again to try an recreate the wonderful feelings I had the first time.

[rajeevk]

There is a saying that you can walk into pluming volcano if you had done your maths right ...

The way you used those parentheses i was stunned ... I m sure that saying about pluming volcano was right.

[desrepeerc]

Great video! It looks like the quiz isn't loading for this one, at least for me.

[one_logic]

I have a question. If addition is a map from the cartesian product ℕ0×ℕ0 to ℕ0, that would mean the sets 2+2 and 4 are equal. Then, what is the expression 2+2? If its a cartesian product, then it would be a set or ordered pair. The problem is that this set, by definition of equality, is not equal to 4 because they do not contain the same elements as {2, 2} ≠ {0, 1, 2, 3} and {2, {2, 2}} ≠ {0, 1, 2, 3}. So, is the definition of equality for natural numbers just defined differently from how it's commonly defined in set theory?

[htchtc]

Sir, can you elaborate "well defined", please.

[angelr.]

1*m := m ist ein besser erstes Falls. und 0*m = m muss ein Theorem sein.