What is $(x^2)(\frac{1}{x^2})$ equal to as $x$ becomes infinitely large? This simplifies to: ∞ = 0. It only takes a minute to sign up. Rebuttal: But any number multiplied with zero is zero, why is this not the case here? Importance of “gerade” to express “just about to”, Attention for time-series in neural networks. If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity? This can be rewritten as: 0 * ∞ = c And hence it does not apply to infinity. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Is infinity the reciprocal of zero/is zero the reciprocal of infinity? See common false rebuttals. Can we omit "with" in the expression glow with (something)? Reply: You are correct, but infinity is not a number. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. How should this half-diminished seventh chord from "Christmas Time Is Here" be analyzed in terms of its harmonic function? What is infinity times negative number in Limit calculation. Why does Lovecraft write that Mount Nansen (approx. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Infinity Times Zero. Do all threads share the same instance of a heap variable, or have different instances of a heap variable? The difference between “goes to infinity” and “goes off to infinity”? Therefore, zero times infinity is undefined. What would happen if infinity was treated like a number? 9000 ft.) is 15,000 feet high? Do they cancel one another out and equal any number since any number = 0 to infinity) and any number infinity to 0? Consider. In actuality, when any number (including zero) is multiplied with infinity, then the results are always undefined. Since the limit ofln(x) is negative infinity, we cannot use theMultiplication Limit Lawto find this limit. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. 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. What is this part which is mounted on the wing of Embraer ERJ-145? I found that a method I was hoping to publish is already known. We can convert the productln(x)*sin(x) into a fraction: Why isnt $\lim_{x\to 0}\frac{\sin x}{x} = 0$? In this case, there is no fraction in the limit. Why does Chrome need access to Bluetooth? Looking for a function that approximates a parabola. How can I change a math symbol's size globally? What does the circled 1 sign mean on Google maps next to "Tolls"? If a piece of software does not specify whether it is licenced under GPL 3.0 "only" or "or-later", which variant does it "default to"? However, what is $(x^4)(\frac{1}{x^3})$ equal to as $x$ becomes infinitely large? Skipping bolts on seatpost , please help? Were any IBM mainframes ever run multiuser? Since infinity is a concept and not a number, you can't use it as a number in arithmetic. What is $(0)(x)$ as $x$ becomes infinitely large? What is $(x^3)(\frac{1}{x^4})$ as $x$ becomes infinitely large? Why is it that the congruence relations usually correspond to some type of subobject? “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. Why is $\infty \cdot 0$ not clearly equal to $0$? Since we already assumed ∞ - ∞ = 0, then we can substitute to this: ∞ + 0 = 0. "also can 0 and infinity be one an others inverse? Since we know that ∞ = ∞ + ∞, then if we substitute this equation into the first infinity in the equation above, we get: (∞ + ∞) - ∞ = 0. Rebuttal: If ∞ × 0 ≠ 0 \infty \times 0 \neq 0 ∞ × 0 = 0, then 0 ≠ 0 0\neq 0 0 = 0. If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity? Which is equal to: ∞ + ∞ - ∞ = 0. Return to the Limits and l'Hôpital'sRulestarting page. infinity times infinitesimal - what happens? What would be a proper way to retract emails sent to professors asking for help? What is this hole above the intake of engines of Mil helicopters. Did people wear collars with a castellated hem? Test null hypothesis that the mean value is less than 60. The same can be said of $x^4$ and $\frac{1}{x^3}$. Does it make sense? Are broiler chickens injected with hormones in their left legs? However, I invite you to ponder these questions: As $x$ becomes infinitely large, the function $x^2$ increases to infinity, but the function $\frac{1}{x^2}$ gets closer and closer to zero. Do they cancel one another out and equal any number since any number = 0 to infinity) and any number infinity to 0? Is whatever I see on the Internet temporarily present in the RAM? $0 \cdot \infty$ object. "also can 0 and infinity be one an others inverse?