I'm still getting things squared away after my blogging break, but as a step on the way back toward normal programming, here's a Dorky Poll: What kind of numbers do you most like to work with?
You can only choose a single answer, which I'm sure will come as a disappointment to many of those favoring the later options. You could always vote a second time from a different computer, though...
Triangular, specifically, but I also preferred Real Analysis to most other things in general.
Double precision floating point.
I always liked NaN myself. Division by zero, anyone?
I don't see primes listed... Yes, I know they're a subset of another option, but they're special enough to deserve their own mention.
Numbers that make sense ;). Today's computer kid generation just lost all sense of significant digits, like using an instrument that's calibrated to 0.1% accuracy and then presenting a report discussing the variations in the 5 - 8th digit. Just because that's what the computer spits out after an A-D conversion, so that's the precision of the measurement, and the randomness has to be explained away. Even worse if they "recognize" the discrete values an A-D converter produces as "quantization" of the phenomenon.
Missing options: algebraic and rational numbers.
The brightly colored ones, please...
Don't know about yours, but my classical measurement apparatus does not work with real numbers. It likes rational ones, instead.
Oh, life would be so easy if the guy behind the apparatus were so rational as the numbers he reads!
While I agree with Eric and Don, it is a daily challenge working with a finite model of the reals which is not reflexive and trichotomy does not hold, i.e. x != x may be true, and none of x < 0, x == 0, or x > 0 can be true.
ones that don't require floating point to represent approximate. integers, rationals and fixed-point decimals, that is. bonus points if they don't require bignums either; arbitrary-size integers are cool and all, but limited-size ones are so much faster to work with.
(poll? there's a poll, like with radio buttons and whatnot? it must be getting filtered out by my ad blocking, if so.)
I'm a mathematician, of the algebraic persuation, so I voted 'complex numbers'.
HOWEVER: Numbers are for pussies, it's the mathematical structures built on the basal number systems that are interesting. Algebraists care about (among other things) solutions of polynomials, which makes structures over the complex numbers interesting. Differential geometers only care about the differentiability of their mathematical gadgets, so they work with stuff over the reals. Analysts work with both real and complex analysis. Topologists don't care about numbers, they work in complete generality. Combinatorists work with integers (or natural numbers, strictly speaking). Mathematical logicians work with arbitrary ordinals and cardinals. No one works with pure imaginary numbers.
Also: it's 'octoniOns', complex numbers are not messy (at least not in the 'grey areas' sense), and Ron @10: there is no finite model for the reals, and the rest of your comment is nonsense, so I assume your are pulling an educated trolling.
FWIW, whenever I am asked what my favourite number is, I answer (truthfully), 'n'.
I like round numbers, because sometimes people get a little overly precise. Not long ago I was asked if I was picking the depth to a coal seam (1-2 feet thick*) at the top or bottom of the seam. The seam was more than 1000 feet below land surface and, in the hilly coal country of southwestern Virginia, I'd guess the surface elevation surveyed for the well had an precision of at best +/- 5 feet. I thought to myself, 'what does it matter?'
*American coal and petroleum geologists will go metric when Hell freezes over
The world actually appears to be complex. QED operates over the complex numbers. Strings moving through time sweep out world-sheets which live in Teichmuller Spaces which have a natural complex structure. We may only be able to imagine rationals, but that's our shortcoming.
and Ron @10: there is no finite model for the reals, and the rest of your comment is nonsense, so I assume your are pulling an educated trolling.
Ron's comment makes perfect sense; it's about the problems inherent in using floating-point numbers on computers.
I used quaternians once in my life. it was pretty fun actually. once i got my mind wrapped around it...
My comment was garbled by html parsing. I was referring to IEEE-754 floating point arithmetic, where x != x may hold for NaN (not a number) values of x, and for which all of x is less than 0, x is equal to 0, and x is greater than 0 are false at the same time, since any comparison to a NaN value is false.
Bah, I'm with Kronecker. Give me the integers and thus, the Rationals.