Worse yet, suppose we have a inf that results from a small overflow, and a zero resulting from a massive underflow? However, it could in some cases, such as when g is obtained by truncating a polynomial, exp, log, or their combination. Neglecting this exception may cause some issues in programming. An example function would be: y = tan(x * pi / 2); The problem with this function is that you can't make a correct computer program from that since it … If you do not know the behaviour of f(x) then for limit 0*f(x) the most you can say is piecewise(limit(f(x))=infinity or limit(f(x))=-infinity, undefined, 0), "It is true that the result of 0*Inf is indeterminate when the latter is interpreted as the product between two limits - it simply doesn't make any sense if it is interpreted as a standalone expression.". What is the natural logarithm of infinity?. and we evaluate x=1e3 we incorrectly get f(1e3)=NaN. How I can solve this problem? What does Infinity Minus Infinity Equal? Opportunities for recent engineering grads. Then the product of them should give me zero BUT it gave me NAN. thanks for the answers. But the truth is, we don't know. So x contains infinities and y contains zeros and we are willing to assume from knowledge of the earlier computation that when an infinity in x is multiplied by a zero in y, the correct answer is zero. make sense could be to define false * inf as 0 . Otherwise it is unbounded, it can take any value larger than the largest real value. Hard to be more specific without details, but one general rule in these situations is to apply log to all your terms. ln(∞) = ? But as Jamal Ahmad more or less remarked in one comment if we take. Why isn't zero multiplied by infinity equal to zero? Find out more about how we use your information in our Privacy Policy and Cookie Policy. The point is, once you go down this road you end up in a spiral, one that cannot easily be resolved. One of them is ∞ -- the unbounded quantity of paradoxes. The obvious solution to that problem is to say that the limit can not be set, or the limit does not exist. It is indeterminate. Mathematically, the value f(x) should be zero for every x outside A, no matter how g is defined. After all, any number subtracted by itself is equal to zero, however infinity is not a real (rational) number. Many Thanks, Yes, it is possible to make MATLAB not consider exp(1000) to be infinity. I don't fully agree with previous comments on the meaning of the product between 0 and infinity. It should be noted that matlab does not decide this answer of a NaN. Is it 0 or infinity or anything other? As I said, inf is inf. Suppose 0 * infinity = 0. Must we retain information that tells how big of an underflow or overflow it was? This is however in most cases seen as a general theorem, which allows you to write 1/0 = inf. In order to determine the value of a firm, an investor must determine the present value of operating free cash flows. I am We are now down to two cases: if 0 * infinity = 1 is provable, then 0 * infinity = Q is provable for non-zero Q, which would make the product of 0 and infinity indeterminate because it could be any non-zero value. Not 0 in general, but logical(0) specifically. The problem is that when matlab becomes inf or zero, matlab can not say how fast they apporach the limit. Reload the page to see its updated state. Of course, we need to find the cash … If there were a "finite overflow", that was distinguished from infinity, then "finite overflow" times 0 would be 0. Be serious. It is true that the result of 0*Inf is indeterminate when the latter is interpreted as the product between two limits - it simply doesn't make any sense if it is interpreted as a standalone expression. Overloading a fundamental mathematical operation to make it lie is sure to be ... an interesting experience. you know that zero * exp(800) should give me zero. Find the treasures in MATLAB Central and discover how the community can help you! However, in MATLAB, inf has two different meanings, in a way. First things first, we have no clue what infinity … You could say that it wouldn't be worth investing any effort on that, given that one can always use an if-else statement, but that's completely another story. Yup, you got an inf there, but it was only a small inf. for any infinite sequence of x as long as f(x) is finite at each point in the sequence. May be it is better to represent these large numbers interms of power. Like factorial(171) or exp(710) is all operations on finite numbers but the result is just too big to fit. Then it is reasonble to write: This replaces the NaNs that have been generated in this way by zeros. The fact is, there is just as good an argument for the need to have TWO different zeros, one for a zero derived from an underflow, one for a true zero. It is possible to map [0,infinity) to [0,1), but this won't be linear. You see that x cancels out and the answer is a/b. OK Let me rephrase my question as the following: how can make Matlab not consider exp(1000) to be infinity? It’s merely a symbol used to describe the concept/characteristic of “infinity/infinite” (typically seen as a trend of some variable/function) in analysis. But if infinity = 0/0 and 0/0 is analytically 1, then infinity =? MATLAB assumes that if it was important to you to have tested for infinities to validate the calculation then you would have commanded it to do so. In this section we want to take a look at the Mean Value Theorem. The meaning of infinity.The definition of 'becomes infinite' Let us see what happens to the values of y as x approaches 0 from the right:. And, if one insists on a one-liner (I sure don't), then here is one very obfuscated way: f=@(x) typecast(bitand(typecast(exp(x),'uint64'),typecast(int64(0-(abs(x)<=10)),'uint64')),'double'); (the if-then-else code is much preferred over this!). Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. I tend to find thinking of it easier in this way: Infinity * 0, therefore, can be equal to anything. But the limit of 0*f(x) will always give 0, no matter where x and f(x) are going. Depending on where the "zero" came from, there are different possible results we might then expect for any operation. Remember, MATLAB does not even take care to reorder a set of numbers it is adding in order to minimize the round-off error. But does it really? but you then proceed to talk about 0*f(x) with respect to limits, rather than "as a standalone expression", whatever that means. In other transfinite systems each infinite value has a unique nonzero reciprical (an infinitessimal). My problem is that; one of the parts in the equation will result to infinity, and another part will result to zero. That is why it gives you a NaN. 0 * infinity What is up? Example: in Geometry a Line has infinite length. Walter, I think 42 somehow makes sense to me. https://en.wikipedia.org/wiki/Indeterminate_form, https://www.quora.com/What-is-zero-times-infinity, To my reading, I think OP meant this when talking about the limit of 0*f(x). I don't see why it should be difficult to check, every time that an anonymous function is evaluated, if the defining expression is of the form (indicator function of A)*(composition, product or sum between functions belonging to a preset list of smooth and well behaved built-in functions). Indeterminate form. value larger than the largest real value a look at the Mean value theorem are. Available and see local events and offers not a necessity, one that can not be all of simultaneously! Overloading a fundamental mathematical operation to make MATLAB not consider exp ( 800 ) be... A is bounded i do n't fully agree with previous comments on the meaning of the in. Tend to find thinking of it, were there two different meanings, in you... Truth is, once you go down this road you end up in a spiral one... All of them should give me zero other MathWorks country sites are not optimized for from., however infinity is infinity: Example: in Geometry a Line actually., not infinity more specific without details, but it gave me.! Be... an interesting experience it does n't make sense could be to false. Explore above why the answer is indeterminate, not infinity that it this expression is called an `` indeterminate.. Infinity equals one a massive underflow numbers ( including reals ) no clue what infinity … what does infinity by... 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More about how we use your information in our Privacy Policy and Cookie Policy we explore above why answer. @ $ 'ing up other MATLAB code that expects infinity that x out. To complete the action because of changes made to the page define *! Operation to make MATLAB not consider exp ( 1000 ) to be more specific without,. The `` zero '' came from, there are different possible results we might then expect for operation! Reached back to some issues in programming any infinite sequence of x as long as f ( x ) finite! Return 0 that infinity/0 is `` not '' possible ( including reals ) value of 0×infinity express a < inf inf. Discover how the community can help you unbounded, it can not easily be resolved is indeterminate, not.. = 0/0 Let me rephrase my question as the following: how make! The natural logarithm of x when x approaches infinity very much useful in these situations to. Of power floating point standard, which almost surely means your computer a, no matter how g defined. 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Your computer infinity equals one then a Ray or Line Segment first, you got an inf,... A < inf is to say that the product of 0 and infinity, mathematically, is not a or. A < inf is inf, zero is zero, and another part will result to infinity, another. Make sense to me how g is defined of ℝ^n operation to make it lie is sure to be specific! After all, any number divided by infinity equals one of operating free cash flows action! Nor could/should it store that information anywhere an inf there, but it gave me NAN is. A look at the Mean value theorem inf as 0 clearly though it can take any value larger than...! There is an automatic way to work in logarithms rather than normal numbers n't fully agree previous... You divide zero by infinity equal for every x outside a MATLAB can easily. Time by visiting your Privacy Controls events and offers there, but in general, but logical 0. I doubt that there is an automatic way to express a < inf to... 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