MathFoundations2: Arithmetic with numbers

We introduce the two basic operations on natural numbers: addition and multiplication. Then we state the main laws that they satisfy.

Category:

Science & Technology

Tags:

• Foundations
• mathematics
• natural
• numbers
• addition
• multiplication
• laws
• Wildberger

[fantasmas9]

I'm just starting to watch this series, after taking a look at the one on Algebraic Topology, and you seem a bit, say, unorthodox, in your ideas about the foundations of mathematics. However, I'm looking forward to watching all of your videos in order to understand your point of view. Would you call yourself a finitist or something in that vein?

And, of course, thanks a lot for posting all of this material. It can be incredibly useful.

[njwildberger]

Hi fantasmas9, I am not really a finitist. Mathematics should not have much to do with belief systems, which such terms suggest. I only insist that mathematics be completely clear and precise. It is a consequence of that position that I reject `infinite sets' and the current theory of `real numbers'. Should I find anywhere a completely clear and precise explanation of these things, I am happy to change my mind.

[riponKS89]

I wish you were my math teacher when I was young.

[njwildberger]

Hi riponKS89,

Thanks. I wish I had a maths teacher, or professor, tell me these things too, it would have saved me a lot of time!

[Junkbox09]

hi norman, shouldn't there also be an identity element for addition, i.e. 0? just checking, because that, in my opinion, would be essential for proving all the laws of addition and multiplication...

[jehovajah]

I will correspond with you by email if i may, as i do not wish to create the wong impression of the excellent approach you are taking. Keep up the great work, and i can promise your viewers a treat when they get to Eudoxus!

[jehovajah]

I am in no way being derisory, but pointing to the archaeological evidence of sophisticated star maps and art in the stoneage cultures. Geometrically, lessons one and two are patently obvious and easily assimilated. The fact that Bombelli and Hamilton had to define these explicitly, has to do with the changing nature of pedagogy and proof due to the abstractness of Al Jibr, the indian style of calculation and the subasutras.

[jehovajah]

So i waited for this one to see how you would develop it. As i pointed out in the first video you were off on the curriculum route, and this confirms it. Although i applaud your revisionist , enrichment approach, i am more in tune with a reversionist approach. In lecture one you missed the key insight which is the foundation notion is not number but measurement of "geometry", geometrical relations. As a consequence you are at kindegarten level in all ancient cultures including stoneage!

[sebil19]

you dont have to go that far i think it would be beneficial to all students if their teachers gave them links to entertaining yet informative online lessons like this one! (especially in times where schools' budgets are being reduced)