MathFoundations4: Subtraction and Division

Subtraction and division are inverse operations to addition and multiplication. Part of a series on the foundations of mathematics

Category:

Science & Technology

Tags:

• Subtraction
• division
• arithmetic
• mathematics
• Wildberger
• natural
• numbers

[tommyrjensen]

I would criticize the organization of these videos by remarking that those who are genuinely interested in what Norman has to say about the foundations of mathematics are very unlikely also to be interested in how one might explain elementary arithmetic at a fourth grade elementary school level by doing handwaving arguments.

[njwildberger]

Hi Tommyrjensen, If you are genuinely interested in the foundations of mathematics, then you are also interested in the nature of division. It is the simple things that are the most important to get right--- a key insight missing from 20th century attempts to set up proper foundations for mathematics.

[StuballScramble]

@MagneticGuitarist The Yuki people of California, according to Wikipedia, had a number system to the base 8 because they counted on the spaces between the fingers.

What I meant was any base number is arbitrary, but this was not explained to me in primary school, and when I asked my teachers, they did not know the answer.

[MagneticGuitarist]

@StuballScramble We humans use base 10 because we have 10 fingers and 10 toes are you perhaps an alien with only 8 of these appendages attatched to each of your limbs ?

[SMGrawks]

I like these so far! Learning the laws of math in school, it was never explained to me the simple logic behind multiplication or division. We were just told that 14/2 is seven but never what we were actually imagining we were DOING to imaginary numbers of things. Basically we were taught what to believe but not why we should believe them! "Don't think, just do."

[StuballScramble]

Maths is taught very poorly in schools I feel, at least in the UK where I grew up. The base ten used to bother me greatly - mankind seemed to be using an arbitrary number to begin double figures. Any time I tried to articulate this in a question to my teachers none of them were able to grasp what I was on about.

[jwh335]

I'm sure not knowing why they do what they do is gobble-de-gook, as well, as far as they are concerned.

[bitsplit]

All numbers m are divisible by 1 and themselves.

n/n = 1, n/1 = n.

That applies whether n is 1, prime, or composite.

[naechancebairn]

i respect what you are doing but surely this is not for primary school children.This is simple gobble-de-gook as far as they are concerned.

[otherchaz]

Another formulation, a prime number n, is a number that is divisible by 1 and n, where n does not equal 1.

We seek out the inverses of our arithmetic operations. Addition suggests subtraction, multiplication suggests division.We discover the new operations do not always have answers that are natural numbers. Our choices are to be selective about the properties of the numbers we operate on, or to define new kinds of numbers.