The trouble comes of what fills the role of stipulation in everyday usage of a natural language. — Srap Tasmaner
But I don't think there's much stipulation going on. — frank
I'd forgotten Dennis Ritchie talks about that, but computer scientists (not coders) spend a fair amount of time thinking about semantics. When Jim Backus and his team at IBM invented the first high-level programming language, they had to simultaneously figure out what such a thing would be, and also invented a formal way of specifying its grammar, the Backus-Naur Form still used today. — Srap Tasmaner
What is math's rudder? What necessity would inspire us to talk in terms of +0? — frank
If you need to say every integer has a sign (for whatever reason) then you'll need 0 to have a sign. Which one? That strikes me as a deep question, in the sense that your reason for giving it a sign is probably not powerful enough to dictate which sign; you'll need some other reason for saying which, and that reason is likely to be "deeper" if you see what I mean. — Srap Tasmaner
Cognitive imperatives? — frank
So, let the domain be the number line and replace A with 0. Clearly each negative number is the image of its corresponding positive value under a reflection in 0 (and vice versa). Now here's the kicker : 0 is a reflection of itself. I.e., 0 is opposite (across from) itself. — Real Gone Cat
frank
No, I was thinking more fundamental mathematical principles, or how mathematics as a system works. Things like harmony, symmetry, orthogonality, duality, that kind of stuff. — Srap Tasmaner
I was addressing the idea that 0 cannot be across from itself. Now you want applications? I don't get you at all. — Real Gone Cat
Then I take it you don't recognize pure math as having meaning — Real Gone Cat
Aren't those things features of how the human mind works? — frank
Actually 0^0 is called indeterminate and has no value. Any rule you're trying to use to assign a value is not applicable. — Real Gone Cat
We have some basic intuitions about collecting and counting, about geometry, and so on, and we build mathematics out of those by making choices, our axioms, and then those axioms have logical consequences. — Srap Tasmaner
A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do. — jgill
↪jgill
Major Edit : "Opposite" is perfectly fine when discussing positives and negatives — Real Gone Cat
How does he know other people exist? — Agent Smith
If you're talking about the axioms that protect set theory from paradoxes — frank
It's debatable whether math really needs set theory as a foundation, though. — frank
You're the one who seems to be insisting that the rules you've mentioned have no use even within the realm of math itself. — frank
Why not use a pair of these? . They are commonly used in math. You could come up with the first being infinitesimals just to the right of zero, etc.
There are your "opposites" of zero. — jgill
No good. 0+ and 0− are used in limit notation to indicate one-sided limits but have nothing to do with opposites. — Real Gone Cat
Okay. But isn't that just to say either there's no math that defines a value for it or that you're unfamiliar with math that does.
To just say, nope, is like saying negative numbers don't have square roots, or, for that matter, that 2 doesn't. — Srap Tasmaner
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