> What I can't do is write a programming language where I use the universally recognised "+" symbols for this operation, call it "addition" and claim that it's totally reasonable.
As a programmer, you're right: we have standard expectations around how computers do mathematics.
As a pedant: Why not? Commonly considered 'reasonable' things surrounding addition in programming languages are:
* (Particularly for older programming languages): If we let Z = X + Y, where X > 0 and Y > 0, any of the following can be true: Z < X, Z < Y, (Z - X) < Y. Which we commonly know as 'wrap around'.
* I haven't yet encountered a language which solves this issue: X + Y has no result for sufficiently large values for X and Y (any integer whose binary representation exceeds the storage capacity of the machine the code runs on will do). Depending on whether or not the language supports integer promotion and arbitrary precision integers the values of X and Y don't even have to be particularly large.
* Non-integer addition. You're lucky if 0.3 = 0.1 + 0.2, good luck trying to to get anything sensible out of X + 0.2, where X = (2 ^ 128) + 0.1.
> I haven't yet encountered a language which solves this issue:
Well, Python supports arbitrary precision integers. And some other niche languages (Sail is one I know).
I don't think "running out of memory" counts as a caveat because it still won't give the wrong answer.
For floats, I don't think it's actually unreasonable to use different operators there. I vaguely recall some languages use +. or .+ or something for float addition.
> Well, Python supports arbitrary precision integers. And some other niche languages (Sail is one I know).
As a Lisper, I very carefully chose an example to account for arbitrary-precision integers (so X + X where X is, say, 8^8^8^8 (remember, exponentiation is right-associative, 8^8^8^8 = 8^(8^(8^8)))).
> I don't think "running out of memory" counts as a caveat because it still won't give the wrong answer.
Being pedantic, it doesn't give the _correct_ answer either, because in mathematics 'ran out of memory' is not the correct answer for any addition.
Right, but you can never guarantee giving the correct answer. What if someone unplugs the power mid-computation? That's basically where running out of memory is (for a modern desktop system anyway).
As a programmer, you're right: we have standard expectations around how computers do mathematics.
As a pedant: Why not? Commonly considered 'reasonable' things surrounding addition in programming languages are:
* (Particularly for older programming languages): If we let Z = X + Y, where X > 0 and Y > 0, any of the following can be true: Z < X, Z < Y, (Z - X) < Y. Which we commonly know as 'wrap around'.
* I haven't yet encountered a language which solves this issue: X + Y has no result for sufficiently large values for X and Y (any integer whose binary representation exceeds the storage capacity of the machine the code runs on will do). Depending on whether or not the language supports integer promotion and arbitrary precision integers the values of X and Y don't even have to be particularly large.
* Non-integer addition. You're lucky if 0.3 = 0.1 + 0.2, good luck trying to to get anything sensible out of X + 0.2, where X = (2 ^ 128) + 0.1.