What is Ln infinity? How to highlight "risky" action by its icon, and make it stand out from other icons? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. depending on the additional definitions/rules you choose. Yes, l’Hospital’s rule applies in this case. If you mean actual infinities, such as the transfinite ordinal number w (omega), your equation still does not hold, for in the surreal numbers, w / (-w) = -1, not -w. Marvin Gardner has a great book, which a believe is called Aha! As infinity is not a specific number it is just an thinking that it is uncountable or a number which we cannot count. A negative infinity, in contrast, is less than every negative real number. Why does Chrome need access to Bluetooth? rev 2020.11.24.38066, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. I.e., infinity divided by negative infinity is -1, not negative infinity. You can use l’Hospital’s rule in such each case above. How do you think about the answers? Were any IBM mainframes ever run multiuser? Why did mainframes have big conspicuous power-off buttons? \lim_{x\to0}g(x) = -\infty Gotcha!, but might be called Aha! Why would I choose a bike trainer over a stationary bike? Because "infinity" is not an actual number, just a concept, there is no number 1/infinity. If you mean actual infinities, such as the transfinite ordinal number w (omega), your equation still does not hold, for in the surreal numbers, w / (-w) = -1, not -w. You can cancel the w's as if they were 2s or something. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Moreover, there are different orders of infinity. To think of it in terms of limits, we approximate infinity to be "a really large number" and negative infinity to be "a really small number". It depends on what you mean by infinity. There's a chance that the approximation will be some fixed value, but there's also a chance it will be negative infinity. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. There are infinitely many real numbers, all of which are finite. Or could be indeterminate. The entry itself is rather useful. If infinity (positive) divides itself by negative infinity, won't it egual negative infinity? I.e., since such a definition would be given for the sake of completeness and coherence with the fact "the limiting ratio is the ratio of the limits", your Infinity divided by a negative finite number is minus infinity (I / -f = -I); 7. The thing is, you can't casually talk about infinity as if it were a number. Ron. We divide 12 by 3 to get 4; the number 3 can't divide anything; it isn't a sentient being, and neither can infinity. That's not a rigorous definition of infinity, but that's what most people are tihnking of when they ask questions like tihs. If you mean actual infinities, such as the transfinite ordinal number w (omega), your equation still does not hold, for in the surreal numbers, w / (-w) = -1, not -w. Negative sign will sit in the beginning of the expression, but infinity/infinity is an undefined number, NOT infinity. Asking for help, clarification, or responding to other answers. In calculus, one considers limits; to say “X approaches infinity” means to consider what happens as X takes on ever larger finite values. so u can't use the L'Hospital's rule here. Actually the quotient infinity / (-infinity) is indeterminate and could be any value, including infinity. however you can sometimes say that the limit of (inf/-inf) -> -inf, for instance lim x->0 ( 1/x / -1/x^2 ) = -inf. Join Yahoo Answers and get 100 points today. Infinity divided by a positive finite number is infinity (I / +f = I); 6. However, it is possible to say that the LIMIT of 1/x, as x goes to infinity, is 0.

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