Again, unified syntax for operators and functions.
Lack of an operator shouldn't specify multiplication. It should specify concatenation. So if x=[1,2] and y=[3,4,5], then xy equals [1,2,3,4,5]. Concatenating reals doesn't really make sense but "concatenation" could be extended to a number of cases: vectors, matrices (l by n and m by n becomes a l+m by n), sets (union), and functions (gf becomes f(g(x))).
Name "real" and "imaginary" numbers to "parallel" and "perpendicular".
I vote 12 as the default base. 30 (2 * 3 * 5) seems too large (900 entries in the multiplication table) and 6 too small (memorable phone number space would be just 279,936).Edited - section removed due to misunderstanding of math terminology
skeptical scientist wrote:No. Equality is not an operator, and you can't write a b = for a = b. You just... can't.
You're right: it's two
. It takes two self comperables and returns boolean value. I would like to see pure math have separate declarative and descriptive equalities. Though unlike programming, it'd give "=" to descriptive since it's used as such in most statements in most proofs I've seen. I'd also eliminate the word "let" from every declarative equality. So "Let f(x) = x2
- 3x where x within R" would become "f(x within R) ¥ x2
- 3x", with a better declarative equality symbol than "¥". Also "within reals" would be implied if type of x isn't stated.
I like postfix for one place functions. So for "( (x) g ) f" the information is in the same order as used for computation.
Infix for 2 place, keep parentheses as a disambigifier. Functions with no arguments are treated as first class functions and are themselves arguments.
Three place functions are badly specified and common ones should be restructured to two place. So
Integral (a,b,f(x)) would become
f Integral (a range b )
We also have conventions where a,b,c... are constants; f,g,h... are functions; x,y,z... are variables; S,T,U... are sets; etcetra. We should have symbols for the main groups that we can append to the names when we want to be explicit.
The thing about recursion problems is that they tend to contain other recursion problems.