Having a little fun with the basics tonight

[Kinma]

@zvuv

I was joking about the ‘mistake’, of course.

Sometimes I am too serious.

@zvuv

Perhaps we can use the word ‘position’ or ‘position field’ as a notation agnostic way of referring to each power of ten.

We can. Also; keep in mind that it is some times useful - when working with two digits at a time, to have 2 digits in a position. For example here:

Help choosing a system for mental math

Yes. 25 - or a little further - is a good first stop. The reason is that there are another two shortcuts for calculating squares. For numbers close to 50 you can use: 25 + x | x^2 Where x is the distance from 50. 56^2 = 25 + 6 | 6^2 = 31 | 36 = 3136 66^2 = 25+16 | 16^2 = 41 | 256 = 4356 43^2 = 25 - 7 | 7^2 = 18 | 49 = 1849 See how easy this is? For numbers close to 100 you can use: 100 + 2x | x^2 where x is the distance from 100. 97^2 = 100 - 2*3 | 3^2 = 94 | 09 = 940…

@zvuv

I’m considering changing the precedence so a squared term in a position doesn’t need parens eg (m,n)2 = m2 ,2 m n , n2
But I am nervous about fiddling with a well tried order.
I also avoid try to avoid implicit multiplication since this is ambiguous when also using single letters to denote a digit

is 2mn the generic form of some number in the 200’s range or is it 2 x m x n?

I would see 2mn as 2 * m * n.

@zvuv

I really like the way it makes negative coefficients seem so natural.

It makes it easy to work with numbers in compliment form which exposes some simple, useful
symmetries and the compliment structure is preserved in the answer

7 = 1,-3 7*13 =(1,-3)(1,3) = 1,0,-9 = 91

Love it.