oops, aeronautics, slight typo.

You know, in all of my years of math, it never came up.

No parts of nothing is nothing.

No parts of nothing is undefined/indeterminate. The not-divide-by-zero rule takes precedence.

And don't confuse zero with the empty set. Zero is not nothing, they're different, mathematically.

@Diplofool - Impossible, and aren't you retired from gaming or the forums or something? How could you have an advanced Engineering degree and never have taken classes and learned concepts that I learned in High School fer cryin' out loud!

Draugnar quite a few internet sites that discuss this question and use the term undefined, as has Diplomat1824 (Dipofool strikes me as unnecessarily unpleasant). Presumably a few of these authors have studied pure mathematics.

What I am saying is that I don't know the answer to this question, but I do think Diplomat has the right to say what he thinks without being ridiculed. Especially as the answer he has offered is the same as offered by many others.

Sorry, but he will always be Diplofool to me. And I don't have a problem wiht him answering, it's his indecisiveness when he claims to have a PhD in Aeronautics and claims the issue "never came up". It had to have come up at some point. Maybe not the undefined vs. indeterminate, but the idea of indeterminate/undefined numbers MUST have.

Additionally, he announced his retirement from the games or the forums (I forget which he announced was his final decision) a few weeks back yet here he is posting AND he just did one of the newest dumb opening in a brand new game within the lats couple of days. So he lied (no surprise) about retiring.

Well Draug, I haven't heard him make a stupid comment on the forums for months, so I'd join the ranks who hope you'd lay off him a bit!
Also, he's virtually silent on the forums, only speaking rarely to give support to a someone else's suggestion, which is neat, clear and short.

OK, since you asked Fig... I'll be nice and refer to him by Diplomat. But I still question his veracity of not having dealt with indeterminate numbers but having a PhD in Aeronautics...

Technically it isn't a lie if he just changed his mind. Maybe he thought he could put diplomacy down but couldn't get over the cravings.

Frelock, I take issue with your use of l'Hopitals rule. You're not truly dividing 0 by 0, you're dividing limits to functions which happen to be 0. It's one thing to say 0/0= whatever and it's another thing to say limit of x/x as x approaches 0 = 1, or limit of x^2/x as x approaches 0 = 0. The limit of both x and x^2 as x approaches 0 is 0 but the value of both functions at 0 is undefined. As such, I don't believe that 0/0 can really be evaluated using l'Hopital's rule.

I addressed this in my earlier post by pointing out that different variations of limit of f(x)/g(x) where x approaches a, and limits of both f(x) and g(x) = 0 as x approaches a will give various answers so the question remains indeterminate/undefined.

"even irrational numbers don't exist in our universe. we need to stop inventing these abstractions"

All your perceptions, all our science, is all abstraction. Irrational, negative, and imaginary numbers have all proved to be incredibly useful in practice and in predicting the future. Even if they don't strictly have real life equivalents, they represent it well enough to have significant meaning.

Irrational numbers *do* exist, and that is extremely obvious. Even if it turns out that they all actually end (after maybe a trillion digits), it is still useful for calculation purposes to assume they don't.

aoe3rules, by the definitions of mathematics, irrational numbers do not end, else they could be expressed as a fraction, albeit a really long one. It has been proven that many numbers cannot be expressed as fractions of integers, such as pi, e, and sqrt(2). The acceptance of irrational numbers by Arabic scholars in the Middle Ages significantly advanced algebra, which has turned out to be monumentally practical.

Games. I love revealing bullshitters.

(Sicarius)

But, in a desperate attempt to salvage this thread, I will have to say undefined. Anything, including zero, divided by zero is undefined.

You have to be careful with irrational numbers. pi is the ratio of the diameter of a circle to its circumference... on a flat surface.

If the surface is curved (warped) then the ratio changes (and triangles can have internal angles of more, or less, than 180 degrees).

A beachball, cut in half, has edges that form a circle, but if the warped space you measure the diameter in is the inner surface of the beachball then you'll measure the diameter as half the circumference, giving pi == 2. Not irrational at all.

As the most extreme example, the space near and within a black hole is incredibly warped. While the circumference of a black hole can be determined, its radius is infinite, so here pi == 1/∞.

But Chrisp, negative numbers most definitely exist. You can have positive and negative temperatures depending on the scale for one.

Don't mind me, I'm a bit buzzed after losing $300 playing poker last night. Had K6 with two sixes on the board. River hits a K and I go all in. Damned if my opponent couldn't call me quick enough. He had pocket Ks so the K that boated me, 6s full also boated him Ks full. Talking about a massive suck out.

It is correct that irrational numbers, like may abstractions, are useful--essential to our technological society. And of course it's true that by definition (well, by theorem that follows easily from the definition) their decimal representation doesn't terminate, even after a trillion digits.

However, in the physical universe in which we live, it's probably true that irrational numbers don't actually exist. They are measures of other useful abstractions, such as circles. But given finite particle size, true circles don't exist except as abstractions.

From what I think I remember from a few decades ago, physicists believe space itself is quantized. And probably time is, as well. And energy. If in each fundamental attribute of the universe there is a quantum such that all true measures of that attribute are multiples of the applicable constant, then there are no actual irrational numbers.

The first time I played poker, I hated it, and we were only playing for like 30 bucks, and I had the most money. So I went all in and walked away. I was sitting in another room when I heard them say "So, that means (my name) won...."

I never played poker again.

Sounds like a tourny style poker. I don't do tourneys cause idiots do stupid things like not really caring and going all in. I play cash games where you can get up and walk away anytime and if you put a bet of $1000 in, it's actually $1000 dollars. People are a little more conservative and less stupid when they are betting with real money.

Draugnar, I wasn't actually trying to argue that they didn't have physical equivalents, just that it doesn't matter if they don't. For that matter, I would say temperature is a bad example of a physical equivalent of negative numbers because temperature can be measured on an absolute scale, unlike many other things. Yes, you could choose a different scale, but that doesn't change the physicality of temperature such that you can experience any true sort of negative temperature. It's a fabrication of humans.

SpeakerToAliens, yes that's all true and very interesting, but pi is defined geometrically as the ratio between any circles' circumference and diameter in Euclidean space, so while warping changes the ratio, it doesn't change the actual value of pi. Besides, pi has so many usages outside of geometry that it is not usually defined by it's geometric properties anymore but rather it's analytic properties.

I know. As soon as I wrote that, I thought about the fact that temp is a measure of energy and in Kelvin, there can be no negative because 0 K is absolutely no energy and therefore no heat.

Draugnar, ah, that's why you had that second post. Gotcha. That's a bad beat for ya. I play poker occasionally, but always for pretty low bets. I usually win with my friends, but I think that's just because I have a longer attention span and willingness to play the game. After a while, most of them start to get tired of it.

Hey, I won though!

How much total? My best night was $2600 on a $300 max buy-in cash table, I hit five boats in a row and walked away when my next hand was pocket Qs beat by trips 6s. I took the same guy for his max buy-in twice by slow-playing him with those boats. Best hand I ever won was with a Q high straight flush (8-Q of Spades in this case), but I only won about $150 plus the preflop betting and blinds on that hand cause my opponent (had Qs full) only had $150 when he went all in and everyone else folded. Worst loss, but most fun hand was when I was up about $1400 and went all in with a J high club flush off the flop. One guy with $500 called with the A of clubs. The 2 of clubs came on the river giving him the nut flush so that I dropped to only being $900 up after that hand. I walked away later that night about $1100 up.

But for every night I walk away up a grand or more, I have 2 or 3 where I lose the $300 I take to the table. I just never take more than I can afford to lose. But that's another game and another forum.