On that last bit (or byte
) what does "not-a-number" value mean in computer programming terms?
What do you think of Infinity as a concept?
- Thread starter Kyriakos
- Start date
On that last bit (or byte
) what does "not-a-number" value mean in computer programming terms?
Perfection
The Great Head.
On that last bit (or byte
It means it's not a number. That is it's an error code stating something occurred that prevents the variable from holding a numerical value. For example you'd get it for trying to divide by zero.
^Yes i thought of that as a possible (error safeguard) case too (dividing by zero). But what are the larger implications of this computer program concept?
Btw i am not asking so as to randomly get +999 shield in some MMORPG and then sell it for some cash.
Btw i am not asking so as to randomly get +999 shield in some MMORPG and then sell it for some cash.
It's used for values that aren't finite or infinity. For example 0/0 is Not-a-number or "NaN". It can also be used for missing values. There are a number of primative operations that can result in NaN, and in most cases, any operation done on NaN results in NaN. NaN also has the quirk of being unordered with itself, using any relational operator like < and >= results in false. A result of NaN can also be configured to cause a "trap" that executes special code to handle the arithmetic error.On that last bit (or byte
EDIT: By the way, most numbers divided by 0 will be infinity, or -Infinity, not NaN.
onejayhawk
Afflicted with reason
The human mind cannot grasp the nature of the infinite, so this is the way we approach it. It leads to absurdities like .9999... = 1.0. T
here are many "Proofs" of this statement, yet the contradiction is childishly simple (.999... is on an interval open at 1, but 1 is not).
J
warpus
In pork I trust
I disagree that the infinite is so hard to grasp.
0.999... = 1.0 relates to how we choose to define real numbers. Distinguishing between different infinitesimal numbers is rarely useful. Also, in nature, there is always a limit to our precision, so a quantity that is infinitesimally close to another value is not distinguishable.
In contrast, there is no quantity that is indistinguishably close to infinity, so using infinity as a number is more useful. I think theoretical mathematicians avoid using infinity as a number, because for them doing so implies a boatload of baggage. On the other hand, an electrical engineer, for example, may happily assign a resistor a quantity of infinite ohms, and get on with using it.
My idea of infinity stems from something I saw a while ago, a map (below is a more recent version).
Go to some dark lonely place at night and look up at the night sky, and consider that you are standing on a chunk of rock orbiting a star, and to get to the nearest neighbor star in the sky requires traveling for four years at a speed four thousand times faster than we've ever traveled before. And that's within a small portion of a single galaxy that's a hundred thousand light years across (with a couple hundred billion stars), and the blobs in that map consist of thousands of galaxies spanning tens of millions of light years. And that map is a drop of water in the ocean.
Go to some dark lonely place at night and look up at the night sky, and consider that you are standing on a chunk of rock orbiting a star, and to get to the nearest neighbor star in the sky requires traveling for four years at a speed four thousand times faster than we've ever traveled before. And that's within a small portion of a single galaxy that's a hundred thousand light years across (with a couple hundred billion stars), and the blobs in that map consist of thousands of galaxies spanning tens of millions of light years. And that map is a drop of water in the ocean.
In some ways, infinity is easier to grasp than numbers like 1080. Can you imagine 1080 atoms? That's how big the visible universe is. Did you learn anything from seeing that? Can you draw any conclusions from that? We can draw more conclusions from knowing that something is infinite.
warpus
In pork I trust
It just wouldn't work, either. A number is a very static thing. You can point to it and say: "It is exactly x divided by y plus z".. or whatever. Infinity is very different from that.. It isn't the biggest number in existence... You will never reach infinity if you continue adding numbers to eachother. It isn't a number, you couldn't use it in equations as one.
When Engineers etc. use infinity as a number, what they actually mean is they use infinity as a shorthand for a limit that approaches infinity. In a lot of situations this distinction is rather academic, but the models and such only make actual sense when observing limits since infinity isn't a number.
As far as conceptualizing infinity as something other than a mathematical definition, I find it very hard. I think you really have to stop thinking of it as a number at all to deal with it. To me it is just a concept that we can always increase, so infinity itself never shows up, we just know that whatever we have can be made bigger, then we make it bigger.
A lot of the implications are very counter intuitive, for example the rational numbers are dense in the real numbers, i.e. any two real numbers have an irrational number between them. But there are only countable rational numbers, this still blows my mind. The .999...=1 thing is obvious by comparison.
onejayhawk
Afflicted with reason
You prove my point. It is true we do not need to deal with true infinities. To paraphrase NC-1701, we simply use the term to mean as large (or small) as necessary for a given mathematical application. That does NOT mean we grasp the concept. We simply have a useful approximation.
J
I disagree completely. A number is a vague thing, difficult to define. There are different things that may be called infinite, and using infinity as a number may mean that it cannot be used to refer to all kinds of things that may be called infinate. But it can be used to measure, indicate quantity, or convey a particular ratio, all which are things that are ascribed to numbers. It can be a number.
You can't reach i if you continue adding integers to each other either, but we consider i a number. It's not a "Real" number, and unlike any Real number it does not have express an ordering. Infinity is similar. It's not "Real" but unlike i it expresses an ordering. Unlike 1.3 it can express the number of objects in a group.
A number must generally be considered together with the set of numbers it is a part of. So 1 is an integer, but it is also a complex number, and when you think of one as a complex number, you cannot use it to express relational order. Likewise we may think of the set of integers modulo 256 as a set in which "1" has a special meaning and is a number. And just as we can define integers modulo 256, which happens to be how the smallest unsigned numbers in a computer are conceived, we can define IEEE 754 double precision floating point numbers. IEEE 754 double precision floating point numbers can express values in the non uniform range [2.226*10^-308,17976*10^308], plus 0, -0, Inf, -Inf, and NaN. Why should these not be called numbers? They are surely the most used kind of number in modern scientific computation. IEEE 754 defines one set of properties for infinity, with particular rules intended to make them useful to computer programmers and users.
Another set of numbers for which infinity exists are Hyperreal numbers. Hyperreals help realize the distinction between the sum 10^i, and the sum the sum 2^i. The latter sum converges toward infinity much more quickly, as i approaches infinity. Therefore the second some is in some sense greater than the former, and Hyperreals are a way of formalizing that quantity.
In practical considerations, and related to why IEEE 754 defines a set of numbers, quite often you need to compute a rough quantity for an expected result. In this kind of analysis you use the same formula that compute the quantity precisely. However, since the calculation is rough, you don't use the whole set of real numbers and real arithmatic. You may treat 10+10 = 10, because it's the same order of magnitude. And you might treat 1/0 as Infinity. The equations are the same, you're doing algebra the same way. The difference is the rules of arithmetic. It's just easier. Making infinity a number makes this kind of math easier too.
No, said models make less sense, because to understand them with infinity as a non-number you need to understand the concept of infinite limits in calculus. Whereas tell a kid that an open circuit has infinite resistance, and they get that right off.
One thing that is true, Infinity isn't one number. Different concepts of infinity imply different kinds of algebra with infinite numbers. But by doing any kind of algebra on infinity, you are treating infinity as a number. And sometimes that's the right thing to do.
In what way is infinity harder to grasp than 1080? I posit that 1080 is harder to grasp.
Hm, what about a 'definition' of infinity by merely using the more stable/concrete notion of a Limit?
For example you could say that if something in X can never get beyond Y, then anything beyond Y can be said to be beyond a limit, and in this manner at some position where it can never effect what is in X. If you have the concept of a position which can never effect something in your own position, it seems to be a sort of more 'concrete' idea of what an infinite distance can be seen as.
And you can always substitute distance for other things.
The horizon would be such a limit, if you are immobile, or bordering some obstacle which you cannot pass to that direction. Of course this would be a language-based definition in this last example, cause it could happen even in a relatively small environment. But as a concept maybe it also is used as part of the math meaning of infinity (again i will refer to the black holes idea by Einstein and them serving as a point beyond which there is no connection between observers in opposite sides of that barrier- although this may not be true it is a nice example in my view
).
For example you could say that if something in X can never get beyond Y, then anything beyond Y can be said to be beyond a limit, and in this manner at some position where it can never effect what is in X. If you have the concept of a position which can never effect something in your own position, it seems to be a sort of more 'concrete' idea of what an infinite distance can be seen as.
And you can always substitute distance for other things.
The horizon would be such a limit, if you are immobile, or bordering some obstacle which you cannot pass to that direction. Of course this would be a language-based definition in this last example, cause it could happen even in a relatively small environment. But as a concept maybe it also is used as part of the math meaning of infinity (again i will refer to the black holes idea by Einstein and them serving as a point beyond which there is no connection between observers in opposite sides of that barrier- although this may not be true it is a nice example in my view
).Limits and infinity do play a large role in calculus. What you do describe basically coincides with that.Hm, what about a 'definition' of infinity by merely using the more stable/concrete notion of a Limit?
For example you could say that if something in X can never get beyond Y, then anything beyond Y can be said to be beyond a limit, and in this manner at some position where it can never effect what is in X. If you have the concept of a position which can never effect something in your own position, it seems to be a sort of more 'concrete' idea of what an infinite distance can be seen as.
And you can always substitute distance for other things.
The horizon would be such a limit, if you are immobile, or bordering some obstacle which you cannot pass to that direction. Of course this would be a language-based definition in this last example, cause it could happen even in a relatively small environment. But as a concept maybe it also is used as part of the math meaning of infinity (again i will refer to the black holes idea by Einstein and them serving as a point beyond which there is no connection between observers in opposite sides of that barrier- although this may not be true it is a nice example in my view
The horizon of the earth is not at infinity of course, but in art a different concept of a horizon is used. The horizon is the line on the horizontal plane of your eyes, to which all perspective lines of objects parallel to that plan merge. That horizon is infinitely far away.
Yes, and in renaissance painting the line of the horizon played a very crucial role. Moreover, due to the heavy use of geometry in a number of those paintings, the horizon as a concept in art does appear to have some common uses with the idea of "vanishing point", which is also used for infinity in some models.
onejayhawk
Afflicted with reason
Simple, with a small change in your question. Any number can be visualized as a collection of smaller numbers, nested til you get a manageable number of points. So 1081 becomes 10333. The zoom factor is rather simple.
What you cannot visualize is something without an end or an edge.
J
Similar threads
