Cardinal numbers are representations of sizes (cardinalities) of abstract sets, which may be infinite. (many solutions). Infinity isn't it? In other words, there is a way of defining a new function, call it so that for . However, we could say that 1/infinity = 0. It is an indeterminate value like 0/0 infinity / infinity. I hope this helps some! This is why it is by definition undefined, because you can define it in any (well, infinite) number of ways and not just that one way when you start to think about it. If the area of a rectangular yard is 140 square feet and its length is 20 feet. Likewise functions with x 2 or x 3 etc will also approach infinity. Let me try to prove it. It is undefined because any division by infinity is be definition undefined. $\begingroup$ The notation is a bad one, $1^\infty$ stand for a limit like $$ \lim_{x\rightarrow x_0} f(x)^{g(x)}$$ where $\lim_{x\to x_0} f(x)=1$ and $\lim_{x\to x_0} g(x)=\infty$ $\endgroup$ – Dominic Michaelis Mar 3 '13 at 20:23 However, 1 divided by ∞ does equal a limit approaching 0. Using some high-powered mathematics (known as complex analysis, see the box) there is a way of extending the definition of the Euler zeta function to numbers less than or equal to 1 in a way that gives you finite values. For example $\frac{1+1+1+\ldots}{2+2+2+\ldots}=\frac12$? When we're little, we start to count, often using our fingers. How do you think about the answers? It is an idea. Join Yahoo Answers and get 100 points today. In other words: When the numerator and denominator are of equal degree, then the limit as x becomes infinite is equal to the quotient of the leading coefficients. But there is also another thing you can do. This is where a lot of the problem comes in when you begin to consider this. Parcly Taxel. compute the centre of generalized linear group GL(4,F). The same will hold for any non-Archimedean ordered field. I have seen a few others explaining it. Is this right or should I change the exponents? However, in applied sciences, where approximations are often prevalent, 1 / infinity is considered as zero, and the word "undefined" is seldom used. If space is infinite it means that there is no end. But there's a problem with that. However, by the same logic, 2/0 = infinity, and 3/0 = infinity, and so forth. lim n/x x-->infinity = 0 This is simply a matter of mathematical definition more than logic. However, you are correct if you consider limits. The limit of any number n over x as x approaches infinity is in fact considered to be zero. Finally, we also learned that just because the problem involves 1^infinity and it typically gives you an answer of 1, it doesn't mean that your 1^infinity situation will always equal 1. At first, you would think 1 divided by ∞ is equal to 0, however that is not correct because that would mean 0 times ∞ would equal to 1. share | cite | improve this question | follow | edited Sep 26 '17 at 12:08. lim n/x x-->infinity = 0 This is simply a matter of mathematical definition more than logic. Solve the fraction of 1 divided by ∞. It just vanished? Still have questions? 7,201 56. If you divide it into a thousand pieces you won't taste it (1/1000). Actually is 0,00000.....1 = 0 approximately. how much money would i have if I saved up 5,200 for 6 years? Since ∀x: x < x + 1 is a first-order sentence holding for reals (as it follows from the ordered field axioms), adding one to an infinite hyperreal produces infinity. This is also true for 1/x 2 etc : A function such as x will approach infinity, as well as 2x, or x/9 and so on. Get your answers by asking now. So i think 1/infinity is undefined. The limit of any number n over x as x approaches infinity is in fact considered to be zero. However, some of them are a bit wrong about the explanation since the question itself is wrong. And if we have an infinity divided by another half-as-big infinity, would we get 2? that is the language when talking about Pure Mathematics. Functions like 1/x approach 0 as x approaches infinity. Did McCracken make that monolith in Utah? Science Advisor. Black Friday starts off with whimper despite record day, No thanks: Lions fire Matt Patricia, GM Bob Quinn, How the post-election stocks rally stacks up against history, Reynolds, Lively donate $500K to charity supporting homeless. If 1/infinity=0, then 1/0=infinity. Problem 4. Anything divided by 1 just stays the same. Also need help finding the volume please? Think about it. However, by the same logic, 2/0 = infinity, and 3/0 = infinity, and so forth. Thus, infinity*0 = 2, and infinity*0 = 3 and so forth. Tony Hsieh, iconic Las Vegas entrepreneur, dies at 46, A boxing farce: Ex-NBA dunk champ quickly KO'd, Jolie becomes trending topic after dad's pro-Trump rant, 2 shot, killed at Northern Calif. mall on Black Friday, Harmless symptom was actually lung cancer, Eric Clapton sparks backlash over new anti-lockdown song. calculus sequences-and-series infinity nonstandard-analysis. Infinity isn't a number but it just means it doesn't end. By the same logic, 1/0 = infinity and maybe more interestingly, infinity*0 = 1. And that is proven not true here. strictly speaking, 1 / infinity is infinitesimal (very small), and 1 / undefined is zero. Unless you mean 1 over infinite, in which case the answer is zero. 71.2k 14 … If we divide 1 by infinite number of pieces and they end up with zero each, then what happened with 1? Can science prove things that aren't repeatable? In other words, 1 divided by ∞ does not equal a number or is undefined No 1^infinity is not equal to 1. 1/infinity is infinitly small so it can be treated as zero. But be careful, a function like "−x" will approach "−infinity", so … However, if we have 2 equal infinities divided by each other, would it be 1? it's a subtle difference,but 1 / infinity is undefined (because infinity is not a single number), however, the limit of 1 / x as x ==> infinity is indeed 0, the only way a fraction can be exactly 0 is if the numerator (top) is 0, and 1 can never be 0 in this numerator, => 1^infinity=any natural no. Mathematics. Infinity is actually not a number just like what @paston rotar was saying. and for the function has well-defined, finite values. Find its width.? I assure you, 1/infinity≠0. For the best answers, search on this site https://shorturl.im/qimtd. One positive integer is 7 less than twice another. In mathematics, infinity plus one has meaning for the hyperreals, and also as the number ω+1 (omega plus one) in the ordinal numbers and surreal numbers.. Gold Member. Just saying. By the same logic, 1/0 = infinity and maybe more interestingly, infinity*0 = 1. However, by the same logic, 2/0 = infinity, and 3/0 = infinity, and so forth. = = = 0. If you have a cake and you divide it into 4 pieces, it is tasty (1/4). There are several mathematical theories which include both infinite values and addition. The limit of any number n over x as x approaches infinity is in fact considered to be zero. lim n/x x-->infinity = 0 This is simply a matter of mathematical definition more than logic. The sum of their squares is 145? 1/infinity is Not equal to zero 1/infinity is not a number however limit x->inf 1/x = 0 there's a key difference &infinity; &inf; fty &fty; Mar 27, 2003 #8 Integral. Staff Emeritus. You can sign in to vote the answer. By the same logic, 1/0 = infinity and maybe more interestingly, infinity*0 = 1.
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