3 ms·
Well, we could use = explicitly. Write a blank in an equation to mean "the thing that fills in this blank", ex. [_+1=2]=1. So x^y = [x^y = _] z^(1/y) = [_^
by edflsafoiewq 6y ago
Well, we could use = explicitly. Write a blank in an equation to mean "the thing that fills in this blank", ex. [_+1=2]=1. So
x^y = [x^y = _]
z^(1/y) = [_^y = z]
log_x(z) = [x^_ = z]
The first four identities from the post are
[x^_ = x^y] = y
x^[x^_ = z] = z
[_^y = x^y] = x
[_^y = z]^y = z
The next two are (the nested [] confirm these are more complicated)
[[_^y = z]^_ = z] = y
[_^[x^_ = z] = z] = x
Generalizing
[f(x) = _] = f(x)
[f(_) = f(x)] = x
f([f(_) = x]) = x
[f(_, [f(x, _) = y]) = y] = x
- jerf 6y ago"Write a blank in an equation to mean "the thing that fills in this blank", ex." Hmmm... I think I want something other than "a blank", but there's some promise there. I feel like your suggestion has the advantage of humbly composing with all the existing notation, whereas the triangle idea itself seems to kinda arrogantly supercede it and rewrite how equations work for just that one operator. (I've add some leading adjectives to indicate how it sort of feels to me.)