0/0 is not defined. That's all. Now you could have two functions f(x) and g(x) such as their limite is equal to 0 when x is close to 0, and you're trying to look if f(x)/g(x) is defined for x close to 0. For example I can take f(x) = x and g(x) = x , I'll have f(0)=0 and g(0)=0 however if I calculate for any x different of 0 f(x)/g(x) = 1 , for x=0 it's still undefined but the limit of f(x)/g(x) as x goes close to 0 is 1. Now could do the same with f(x) =2x and g(x) = x. The limit at 0 of f(x)/g(x) = 2. In fact you could do this with any number a and have f(x)=ax and g(x) = x, the limit would be equal to a. But there are also tons of example where the limits is not finite f(x) = x and g(x) = x² then f(x)/g(x) = 1/x doesn't have any limit at 0. Conclusion : if you have a 0/0, it will always depends on the function you study, there are no general solutions to this limit Answer from Ulzaf on reddit.com
0/0 is not defined. That's all. Now you could have two functions f(x) and g(x) such as their limite is equal to 0 when x is close to 0, and you're trying to look if f(x)/g(x) is defined for x close to 0. For example I can take f(x) = x and g(x) = x , I'll have f(0)=0 and g(0)=0 however if I calculate for any x different of 0 f(x)/g(x) = 1 , for x=0 it's still undefined but the limit of f(x)/g(x) as x goes close to 0 is 1. Now could do the same with f(x) =2x and g(x) = x. The limit at 0 of f(x)/g(x) = 2. In fact you could do this with any number a and have f(x)=ax and g(x) = x, the limit would be equal to a. But there are also tons of example where the limits is not finite f(x) = x and g(x) = x² then f(x)/g(x) = 1/x doesn't have any limit at 0. Conclusion : if you have a 0/0, it will always depends on the function you study, there are no general solutions to this limit Answer from Ulzaf on reddit.com
Reddit
reddit.com › r/learnmath › is 0/0 = infinite ?
r/learnmath on Reddit: is 0/0 = infinite ?
January 6, 2021 -
I saw too many people saying this statement is true but its not I can prove it. Sometimes you find the limit of a function with an "a" integer 0/0 so you change the function form and make with a known form and limit of a/0+ is infinite there cant be 0/0 is infinite ..
Top answer 1 of 6
32
0/0 is not defined. That's all. Now you could have two functions f(x) and g(x) such as their limite is equal to 0 when x is close to 0, and you're trying to look if f(x)/g(x) is defined for x close to 0. For example I can take f(x) = x and g(x) = x , I'll have f(0)=0 and g(0)=0 however if I calculate for any x different of 0 f(x)/g(x) = 1 , for x=0 it's still undefined but the limit of f(x)/g(x) as x goes close to 0 is 1. Now could do the same with f(x) =2x and g(x) = x. The limit at 0 of f(x)/g(x) = 2. In fact you could do this with any number a and have f(x)=ax and g(x) = x, the limit would be equal to a. But there are also tons of example where the limits is not finite f(x) = x and g(x) = x² then f(x)/g(x) = 1/x doesn't have any limit at 0. Conclusion : if you have a 0/0, it will always depends on the function you study, there are no general solutions to this limit
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5
It's either undefined or indeterminate, depending on the circumstances.
Wikipedia
en.wikipedia.org › wiki › Division_by_zero
Division by zero - Wikipedia
1 week ago - Since any number multiplied by ... input tends to some value. When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large, and is said to "tend to infinity", a type of mathematical ...
Videos
04:40
I Finally Found Out What 0/0 Should Be - YouTube
12:33
Indeterminate: the hidden power of 0 divided by 0 - YouTube
Why can't we divide by 0? (The difference between 1/0 and 0 ...
04:47
0 ^ ∞ , It's What You Think - YouTube
This limit has 0^0 indeterminate form but the answer is 0 - YouTube
0 divided by 0 (when should we say "undefined" vs "indeterminate") ...
Quora
quora.com › Is-0-0-undefined-1-or-infinity
Is 0/0 undefined, 1, or infinity? - Quora
Answer (1 of 15): \frac{0}{0} in of itself is meaningless. A rational number cannot have a zero in the denominator. Supposing that we did want it to make sense it would have to be a solution to x \cdot 0 = 0 Well, any real number times zero is zero, and we would like division to give a unique ...
Stack Exchange
math.stackexchange.com › questions › 1411416 › why-zero-divided-by-zero-is-undefined-and-not-infinity
divisibility - Why Zero divided by Zero is undefined and not Infinity - Mathematics Stack Exchange
When we divide one number by another we must get, again, a number; say, real numbers. Since infinity is not a number, it does not make sense to say 0/0 = infinity. Think of a/b to be the number c such that a=bc.
Medium
prabhatmahato.medium.com › why-is-any-number-over-0-undefined-or-what-we-say-infinity-5318dc5b0153
Why is any number over 0 undefined or what we say infinity? | by Prabhat Mahato | Medium
March 31, 2023 - 1/1=1, 1/0.1=10, 1/0.01=100, 1/0.001=1000, 1/0.0001=10000 Here, the value of the expression goes on increasing when we decrease the value of denominator. So, when the value of denominator tends to or equals to zero, then the value of the expression tends to or becomes so large that we cannot find it’s bound or in others it becomes infinity i.e., 1/0=∞.
Snap! Forum
forum.snap.berkeley.edu › computer science › math
∞ and NaN - Page 2 - Math - Snap! Forum
December 15, 2023 - Not true. Also, @anon45095554 said that 0^0, 1/0, and the 0th root of a number involve infinity, but I don't know how that could be.
YouTube
youtube.com › watch
1/0 = infinite is explained | Breaking the rules of Mathematics. - YouTube
Have you ever wondered why 1 divided by 0 equals infinity? In this video, we will explain the reasoning behind this common mathematical phenomenon.In general...
Published March 19, 2023
Math Central
mathcentral.uregina.ca › qq › database › qq.09.98 › dixon4.html
Indeterminate forms
What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" ...
LinkedIn
linkedin.com › pulse › infinity-equal-0-zero-artofchilling-org
Is ∞(Infinity) equal to 0 (ZERO) ?
November 8, 2020 - This is not something that you believe or choose not believe. It is the truth, however weird or abstract it may seem. The symbol zero (0) and Infinity ( ∞) were given to the world by eastern sages who experience this reality.
Physics Forums
physicsforums.com › mathematics › general math
Dividing by Zero: Is it Undefined or Infinity? • Physics Forums
December 7, 2004 - Calculus, on the other hand, which ... infinities, only multiplying and dividing them, but in Quantum Physics, infinity - infinity does equal 0....
Reddit
reddit.com › r/math › is 0 the same as infinity?
r/math on Reddit: Is 0 the same as infinity?
June 17, 2016 -
Might seem dumb but the more I think about it the more I'm not sure. Isn't 0 an infinite number on it's own? Anything times 0 is 0, and an infinite amount of nothing is still nothing. So infinity times 0 should still be 0 right?
I was trying to figure out if 0 is actually a correct or technically correct answer to giving someone an infinite amount of something.
Like for instance, if I wished to a magical genie for an infinite amount of money and the Genie gave me nothing, isn't that an infinite amount of money as nothing is the same as infinity?
Am I totally wrong?
Top answer 1 of 5
18
Isn't 0 an infinite number on it's own? No. In what way, pray tell, is 0 infinite? Is 0 the same as infinity? No. If this above is your only argument, and it relies on the assumption that 0 is infinite, that is one letter off from being circular logic.
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17
Yes, you're totally wrong. First of all, infinity is not a real number. You can't say "infinity times 0" or "infinity times 3" or "infinity minus 2" and expect it to be meaningful. There are ways to formalize the idea with alternative number systems that contain infinities, but then you typically can't just say "infinity". You have to refer to a specific infinite number. (And then you run into problems with not being able to do division or even subtraction in some cases.) You can also formalize the idea with limits, the tools that we use as the foundation of calculus. That still doesn't mean that 0 is an infinite number though. 0 is finite. It's less than 1, which is also finite.
Physics Forums
physicsforums.com › mathematics › calculus
Why 1 / ∞ = 0 but ∞ * 0 is not equal to 1? • Physics Forums
December 20, 2021 - As we know those relations are true: if a/b = c, then a = b*c and b = a/c Therefore if 1/ ∞ = 0, ∞ * 0 should be equal to 1 and 1/0 = ∞ ... Division by zero or by infinity is undefined because they lead to mathematical inconsistencies ...
Top answer 1 of 13
93
The other comments are correct: $\frac{1}{0}$ is undefined. Similarly, the limit of $\frac{1}{x}$ as $x$ approaches $0$ is also undefined. However, if you take the limit of $\frac{1}{x}$ as $x$ approaches zero from the left or from the right, you get negative and positive infinity respectively.
2 of 13
89
$1/x$ does tend to $-\infty$ as you approach zero from the left, and $\infty$ as you approach from the right:
That these limits are not equal is why $1/0$ is undefined.
Friesian
friesian.com › zero.htm
Zero Divided by Zero
It will become larger as y gets smaller. As y approaches 0, x/y will become indefinitely large. The obvious step to take, which I think had already occurred to my friends and me in Junior High, would be to say that x/0 is infinite -- we had a natural impatience with this "undefined" business.
Reddit
reddit.com › r/learnmath › why do we say 1/0=undefined instead of 1/0=infinity?
r/learnmath on Reddit: Why do we say 1/0=undefined instead of 1/0=infinity?
October 24, 2020 -
Like 10/2- imagine a 10 square foot box, saying 10 divided by 2 is like saying “how many 2 square foot boxes fit in this 10 square foot box?” So the answer is 5.
But if you take the same box and ask “how many boxes that are infinitely small, or zero feet squared, can fit in the same box the answer would be infinity not “undefined”. So 10/0=infinity.
I understand why 2/0 can’t be 0 not only because that doesn’t make and since but also because it could cause terrible contradictions like 1=2 and such.
Ah math is so cool. I love infinity so if anyone wants to talk about it drop a comment.
Edit: thanks everyone so much for the answers. Keep leaving comments though because I’m really enjoying seeing it explained in different ways. Also it doesn’t seem like anyone else has ever been confused by this judging by the comment but if anyone is I really liked this video https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:division-zero/v/why-dividing-by-zero-is-undefined
Top answer 1 of 5
7
Because a/b = x which means a = bx. For example : 6/2 = 3 which is same as saying 6 = 2*3. So when we divide 1 (or any number) by 0, it implies that 1/0 = x i.e. 1 = 0*x , which we know is not possible as anything multiplied by 0 gives you 0. Therefore we say it is undefined and not infinity.
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2
Usually it's because infinity isn't an element of the set the division is defined on. If you do include infinity with the reals then there are two common ways to do it. The Affinely Extended Reals, where positive infinity and negative infinity are included. In this case if we allow 1/0=infinity, then 1/(-0) presents a problem since1/(-0)=-1/0=-infinity would be invalid. Alternatively there is the Projectively Extended Reals, where we want 1/0=infinity, so we accept that infinity=-infinity to allow 1/(-0)=1/0. This is equivalent to a number circle, where traveling infinitely far in either the positive or negative direction leads us to the same point.
The Philosophy Forum
thephilosophyforum.com › discussion › 9651 › zero-infinity
Zero & Infinity - The Philosophy Forum
This implies that 0 > infinity. This leads to 1 above (Yes) It's a loop made up of two contradictions viz. 1 and 2. It seems impossible to find or state the magnitude relationship between 0 and infinity. These two are neither equal nor is it that one is less than or greater than the other.
Math Answers
math.answers.com › questions › Why_does_0_divided_by_0_equal_infinity
Why does 0 divided by 0 equal infinity? - Answers
November 11, 2017 - Any number (apart from 0) divided by 0 is equal to infinity.
Superprof
superprof.co.uk › resources › academic › maths › calculus › limits › properties of infinity
Properties of Infinity
Zero divided by a number (e.g. 0 ÷ 5) equals 0. A number divided by zero (e.g. 5 ÷ 0) is undefined. We’ll update the sentence to reflect the correct mathematical explanation. We appreciate you catching that and helping us improve the accuracy of the content! ... There is more than one size of infinity, though.
Khan Academy
khanacademy.org › math › algebra › x2f8bb11595b61c86:foundation-algebra › x2f8bb11595b61c86:division-zero › v › why-zero-divided-by-zero-is-undefined-indeterminate
Khan Academy
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Quora
quora.com › Why-is-something-0-equal-to-infinity
Why is something/0 equal to infinity? - Quora
Answer (1 of 13): Why is something/0 equal to infinity? Adding to other answers, we don’t normally define it, so it’s not really true. Before trying to define a/0 we require a system in which \infty is defined. But \infty is not usually defined to be a number, so a/0 is usually left undefined.