From: Xavier Noria Date: 2010-12-31T04:51:03+09:00 Subject: Re: Numeric comparison with nil - Math masochists only!! On Thu, Dec 30, 2010 at 8:30 PM, Everett L Williams II wrote: > Finite addition, subtraction, multiplication, and division are native > functions of all but the simplest computers, whether the computer is > self-aware or not, silly as that is to even discuss. What we are talking > about here is native instructions as opposed to algorithmic processes. Since > I have been programming computers for 44 years, I tend to think that most > people, at least in these parts understand the distinction. As they say, if > you don't understand it, you can't program it. And, your understanding of it > will be what is programmed. Most of us who have been programming for more > than five minutes know that we must limit our use of an instruction to the > finite limits of the hardware capability. Programmers must constantly be > aware that all processes must be bounded, or programs may loop until > stopped, a condition not desirable, at least in my experience. There is both > a quantitative and a qualitative difference between using the basic > capacities of hardware and instruction sets, and overlaying on those extreme > sets of logic not amenable to any computation. But don't you realize you are doing an interpretation? The computer knows *nothing* about numbers. The computer is a physical machine, numbers are abstractions *you* are putting onto it. I could say that for every representable n, any given native 4-bytes represent the infinite number ∞ + n. By definition (∞ + n) + (∞ + m) = ∞ + (n + m). There you have it, infinite quantities dealt with in a "finite" computer. My ∞ + 0 is no different than your vanilla 0 for a blank 4-bytes. The bytes are just electronics, we are the ones interpreting them in a convenient and natural, but also arbitrary manner.