0 1 is undefined reddit - Brave Search

why is 0/1 undefined?

reddit.com › r › mathmemes › comments › 1c75b1e › why_is_01_undefined

yup, definitely undefined from this view. Answer from Deleted User on reddit.com

reddit.com › r/mathmemes › why is 0/1 undefined?

r/mathmemes on Reddit: why is 0/1 undefined?

April 18, 2024 - However, 1/0 is undefined, so 0/1 is undefined.

reddit.com › r/mathematics › why is 0/0 undefined and not 0 or 1?

r/mathematics on Reddit: Why is 0/0 undefined and not 0 or 1?

December 19, 2018 -

I understand that you can't divide anything by 0, but I can see arguments why it could be 0 (0 divided by anything is 0) or 1 (anything divided by itself is 1). Personally, before I plugged 0/0 in my calculator, I thought the answer would be 0. I'm just curious if there's a special reason why 0/0 is undefined, like how there's a special reason why 1 is not prime.

8/4 = 2 because 4*2 = 8, and 2 is the only number where 4*x = 8. So if you want 0/0 = x, we want that 0*x = 0. So OP, you tell me, what is the only number x where 0*x = 0.

it could be 0 (0 divided by anything is 0) or 1 (anything divided by itself is 1) This should raise a red flag that 0/0 is undefinable already; you have a contradiction arising from two different rules approaching the same thing. Another way to put it: The limit as x goes to 0 of 0/x is 0 The limit as x goes to 0 of x/x is 1 In both cases, you arrive at 0/0 in a perfectly logical manner, and you find that it has two different values. This is a contradiction, so 0/0 can't be given a general definition. Edit: I just saw you are in precalc. You are gonna have a ton of fun exploring indeterminate forms in calculus!

Videos

khanacademy.org

Why dividing by zero is undefined (video)

That's why 1/0 is undefined !!! - YouTube

Is 0^0=1? - YouTube

That's why 0/0 is undefined !!! - YouTube

Can I ask why 1 divided by 0 doesn’t equal infinity? - YouTube

August 29, 2025

1/0 = infinite is explained | Breaking the rules of Mathematics.

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

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.

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.

reddit.com › r/mathematics › why is 0^0 considered undefined?

r/mathematics on Reddit: why is 0^0 considered undefined?

May 22, 2025 -

so hey high school student over here I started prepping for my college entrances next year and since my maths is pretty bad I decided to start from the very basics aka basic identities laws of exponents etc. I was on law of exponents going over them all once when I came across a^0=1 (provided a is not equal to 0) I searched a bit online in google calculator it gives 1 but on other places people still debate it. So why is 0^0 not defined why not 1?

Well sure x0 = 1, but 0x = 0, so what 00 should be ? Convention is 1, because it generalizes well in most cases. I think the reason is, xy tends toward 1 even when x tends toward 0 faster than y. But it's a convention, not a mathematics result, it cannot be proven, it's just a choice.

Here's the wikipedia page on it: https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero "In certain areas of mathematics, such as combinatorics and algebra , 00 is conventionally defined as 1 because this assignment simplifies many formulas and ensures consistency in operations involving exponents ... However, in other contexts, particularly in mathematical analysis , 00 is often considered an indeterminate form ."

reddit.com › r/mathematics › explain why 1÷0 doesn't equal 1

r/mathematics on Reddit: Explain why 1÷0 doesn't equal 1

November 26, 2025 -

Hubby and I were talking about this because we saw a YouTube video that said the answer is 0, but then online or with a calculator it says undefined or infinity. Neither of of us understands why any number divided by 0 wouldn't be the number. I mean, if I have 1 penny and I divided it by 0, isn't that 1 penny still there? Explain it as if we haven't taken college algebra, well, because we haven't.

Thanks!

This is very elementary way of thinking but I believe division is like a handing out problem. If I have 1 cake and split it among 4 people, everyone get’s 1/4 of the cake. But if I have one cake and split it among 0 people, how much does everyone get? Well there’s no people so we can’t really say these nonexistent people get 0 or 1 so the answer is undefined as the people we are splitting it amongst do not exist so they cannot really get anything.

What is 3/2? You can think of it as a number you can multiply 2 by to get 3. 3 = 3/2 * 2 Now 0 times anything is 0 no matter what you multiply 0 by. On the other hand if 1/0 were a number it would be a number such that 0 * 1/0 is equal to 1. But that’s impossible, so 1/0 doesn’t exist.

reddit.com › r/explainlikeimfive › eli5:why is 0 divided by 0 undefined when any other number divided by its self equal to 1?

r/explainlikeimfive on Reddit: ELI5:Why is 0 divided by 0 undefined when any other number divided by its self equal to 1?

June 4, 2014 - If graph the equation x/y=1 then at the origin (0,0), we're ok with saying that 0/0 = 1 because everything else on the line = 1. Vice-versa with -x/y where 0/0 = -1. If you come along the X axis you get where 0/0 will shoot off between +- infinity. And with coming down the Y axis you can get 0/0 = 0. 0/0 represents something that can be a "Removable singularity". And it's a bit weird because the answer to your question is that 0/0 can be whatever you want it to be, depending on which angle you approach it from. This is where the term "Undefined" comes from.

reddit.com › r/learnmath › why can't 1 divided by 0 be infinite

r/learnmath on Reddit: Why can't 1 divided by 0 be infinite

June 19, 2024 -

If I lower down from positive numbers it can be positive infinite, if I lower down from negative ones, it can be negative infinite so one of the proves of it being undefined, why not both, why not simply infinite

You can define operations however you want. However, there is a reason why 1/0 tends to be undefined. Say you define 1/0 to be something, call it a. Now, we would like a to be a number such that when multiplied by 0 yields 1. So 0 = a * 0 = 1, so 0=1. This also means that for any number x, x = 1 * x = 0 * x = 0, so all numbers are zero. This means that if we want 1/0 to be defined, either we have to sacrifice the meaning of division and other rules of arithmetic, or we are working in a number system where all numbers are equal to 0. These reasons are why we generally just tend to leave 1/0 undefined. It creates a mess if we treat it like we would ordinary division. There is value in seeing 1/0 as "infinite", but we need to tread lightly, and acknowledge that the ordinary rules of arithmetic do not carry over.

it can be, provided you explicitly state that you are working with the projectively extended real line rather than the standard real numbers.

reddit.com › r/learnmath › if anything raised to power zero is 1, then why is 0⁰ so controversial?

r/learnmath on Reddit: If Anything raised to power zero is 1, Then Why Is 0⁰ So Controversial?

3 days ago -

I have been thinking about something simple but kind of confusing. We’re taught that any non-zero number raised to the power of 0 equals 1. That pattern seems consistent and works smoothly in algebra. But then comes the weird case: 0 raised to power 0 Suddenly, things aren’t so straightforward. Some places say it’s undefined. Some say it depends on context. Others treat it differently in calculus and programming. Why does the usual “anything to the power 0 is 1” idea seem to break here? What exactly makes this case so special compared to other numbers? I am very curious to hear different perspectives on this.

It conflicts with "0 to any power is 0". Arguments about transsubstantiation vs consubstantiation are less heated.

It's special because there are two conflicting rules: A. Anything raised to power zero is 1 B. Zero raised to power anything is zero So if we have 00, it would be 1 because of rule A, but it would be 0 because of rule B. And that's why it depends on context.

Find elsewhere

Google Bing Mojeek

reddit.com › r/mathematics › if any number divided by itself is 1, then 0/0 should be 1, but its undefined, why?

r/mathematics on Reddit: If any number divided by itself is 1, then 0/0 should be 1, but its undefined, why?

September 21, 2025 -

its my understanding that anything divided by itself is 1, 2/2 is 1 and etc, but anything divided by 0 is undefined, so why is 0/0 not 1, since its 0 divided by itself

but 0 divided by any number is zero. so 0/0 should be 0. if 0/0 should be both 0 and 1, we better leave it undefined.

Your understanding is incorrect. The correct statement is that anything divided by itself is 1, as long as the division operation is meaningful. That last part is often left unsaid as it is asaumed to be understood. Division by zero is not meaningful. (Btw, even here I'm leaving out some things unsaid, but those would be too technical to bring up at this level.)

reddit.com › r/askscience › why is 1/0 undefined, rather than infinity?

r/askscience on Reddit: Why is 1/0 undefined, rather than infinity?

February 20, 2014 - Using the properties of addition ... define 1/0, if you really want to. It's usually undefined because no value for 1/0 is consistent with some of the most fundamental properties of algebra....

reddit.com › r/explainlikeimfive › eli5: why is 1/0 undefined but 0/1=0

r/explainlikeimfive on Reddit: ELI5: why is 1/0 undefined but 0/1=0

February 17, 2025 - When approaching 0 in the denominator ... the negative side, the limit is -infinity. When deviding by 0, the result is ambiguous and that's why 1/0, or anything divided by 0, is undefined....

reddit.com › r/askmath › is this expression undefined or equal to 1?

r/askmath on Reddit: Is this expression undefined or equal to 1?

April 25, 2024 -

This dilemma started yesterday at my high school. We asked 7 teachers how they view this expression. 5 of them said undefined, 2 of them said it equals 1. What do y'all think? I say undefined.

undefined Any function of something undefined is undefined.

Ask the teachers who said it equals 1 if (dog)0 also equals 1. 1/0 is not a number, so the power function is not defined for it.

quora.com › Why-do-some-people-say-that-1-0-is-undefined-while-other-people-say-it-is-infinity-Which-side-of-this-endless-debate-is-right

Why do some people say that 1/0 is undefined while other people say it is infinity? Which side of this endless debate is right? - Quora

In the reals, it’s undefined for the simple reason that there are no infinite reals, and obviously there’s no finite number big enough to be 1/0. But there’s nothing illegal about talking about different kinds of numbers.

reddit.com › r/learnmath › why isn't 0/0=0

r/learnmath on Reddit: Why isn't 0/0=0

November 17, 2023 -

I know very well that x/0 shouldn't be defined for lots of reasons. The limit of aproching it is infinity and minus infinity at the same time; if (x isnt equal to 0) x/0=y than 0y = x which is not possible because it's 0, and more... But there is one exception, and it's 0/0. 0/0 could be any number because 0x always equal to 0. But we can define it to any number we want as long as there is not a contradiction, for example 0! or that square root is only the positive number. And the only number 0/0 could be is 0. And if we think about it, it makes sense. 0/x is always 0, even if we take the limits from both sides it's still 0. And it can't be any other numbers, because if 0/0 = x and we multiply both sides by 2 then 2x = 2*(0/0) = (2*0)/0 = 0/0 = x, and x must be 0. I haven't found any contradictions yet, and there doesn't seem to be any, so why isn't it a thing?

Because division distributes over addition/subtraction 0/0 = (1 - 1)/0 = 1/0 - 1/0 If you have 0/0 = 0 you lose the distributive property, which then causes all sorts of downstream issues.

0/0 = x 0 = 0*x x is any number 0 = 0*1 0 = 0*2 So 1 = 2

reddit.com › r/explainlikeimfive › eli5: why is 0⁰ undefined?

r/explainlikeimfive on Reddit: eli5: Why is 0⁰ undefined?

January 30, 2022 -

Aren't all power's just 1 * x (and then the exponent dictates how many times you multiply by the base)

For example 2¹ is 1*2, or 2.

And 2⁰ is 1, because there are no two's

So shouldn't 0⁰ factor out to be 1 since the exponent basically says 0 is used zero times?

When you try to determine the answer by taking a limit, you get different answers depending on how you construct the problem. If you take the limit of 0x as x approaches zero, you get 0. If you take the limit of x0 as x approaches zero, you get 1. You get the same result from xx as x approaches zero. That said, in many mathematical applications (particularly combinatorics) 00 is defined as being equal to 1; it just makes everything easier.

I don't know if I could explain it like you're 5 but I'll try. 20 = 1 This is because 22 / 22 = 22 - 2 = 1 00 is undefined, however, because: 00 = 02 / 02 = 0/0 Anything divided by 0 is undefined.

reddit.com › r/learnmath › is 0/0 = 1 or undefined?

r/learnmath on Reddit: Is 0/0 = 1 or undefined?

August 7, 2022 -

Hey, I know this might sound like a pretty stupid question but I'm just super curious and couldn't find anything on google that actually helped. For context, I'm in grade 10 (year 11) and I was practicing papers for my math exam which is on Monday and this thought just randomly popped into my head lmao

Considering 0/0, it should be "undefined" as any number divided by 0 is "undefined" right? Even calculators say it's undefined.

but what if I assume a variable, " x = 0 "

Now, x/x = 1 as they cancel each other out

Substituting the value of x as 0, Therefore, shouldn't 0/0 = 1?

So is it undefined or 1?

Undefined. You can't cancel something that is zero. Otherwise (0×3)/(0×1) = 0/0 and is 3 if we "cancel the zeros"

Considering your x/x=1 example, you have to be cautious. A function has a domain over which it will produce a valid output. Assuming we are using the set of real numbers, e.g. y=√x is valid for x≥0 y=1/x is valid for x≠0 y=x/x is valid for x≠0 We often tend to overlook the domain of a function for simplicity but it can cause problems if not considered.

reddit.com › r/askmath › is diving by zero undefined and impossible or is the answer infinity or some other complicated answer taught in advanced math?

r/askmath on Reddit: Is diving by zero undefined and impossible or is the answer infinity or some other complicated answer taught in advanced math?

August 18, 2024 -

Saw 2 people argue whether it can be done or not so I’m curious. One says undefined (which I think the majority of people know the answer as) the other said that actually it can be solved as infinity in advanced math. I wonder if that true and if someone can dumb it down if so

It's undefined. 1/x approaches infinites as x approaches 0 if you come from the positive direction. But it approaches negative infinity as x approaches 0 if you come from the negative direction. It can't be both positive and negative infinity, so it's undefined.

The number system you're most familiar with is the real numbers, or ℝ. ("Real" here does not mean anything about physical existence; it's just a name.) In the real numbers, there is no such thing as infinity. 1/0 is undefined. In higher mathematics, different number systems are used for different purposes. (Actually, this is true in your everyday life, too - you'd probably stick with whole numbers for counting how many people there are, and extend to the real numbers for getting their average height.) We're allowed to define whatever rules we want to extend our number system, as long as we're fully consistent (and clear about what system we're working in). Adding in more numbers typically gives us more possibilities, but also removes some nice laws that make algebra easier. (For instance, one system called the quaternions removes the law that a×b is always the same as b×a. It has some uses, but we don't use it very often, because we like to be able to rely on that law!) Some extensions of the real numbers do indeed allow 1/0, and they make it so that 1/0 is a new number we call "∞". (They typically keep 0/0 undefined, though.)

reddit.com › r/askmath › 0 x undefined = -1???

r/askmath on Reddit: 0 x undefined = -1???

December 10, 2024 -

the formula to determine whether two lines are perpendicular is as follows: m1 x m2 = -1. its clear that the X-axis and the Y-axis are perpendicular to each other, and there gradients are 0 and undefined respectively. So, is it reasonable to say that 0 x undefined = -1?

No it is not reasonable to do that. It is not reasonable to say anything about something that is not defined. “Undefined” is not a quantity, it’s a literal description. The rule you mentioned simply doesn’t work if the two lines are the x and y axes because there does not exist a real number a such that 0a = -1. That doesn’t mean they’re not perpendicular, just that the “multiply the gradients and check if it’s -1” test has a single case where it doesn’t work.

The direction of a vertical line in the y axis isn't undefined, it just cant be defined as a slope, y/x.

reddit.com › r/askmath › is 0/0 undefined

r/askmath on Reddit: Is 0/0 undefined

August 22, 2023 -

I understand that x/0 where x does not equal 0 is undefined because no number multiplied by 0 will give a non-zero product since all products of 0 is 0.

But by that logic, the solution of 0/0 shouldn't be undrlefined, rather have an infinite number of valid solutions since any number multiplied by 0 is 0 and therefore a valid solution for the expression.

I got into an argument with my brother about this but he is very much smarter than I. He insisted anything divided by 0 is undefined and 0/0 is not an exception.

Please advise! Thanks

Your language is imprecise. What does it mean by ‘The solution of 0/0’? This is where students get confused - just because you can string together a seemingly coherent set of symbols doesn’t necessarily mean it’ll represent something meaningful. When you write 0/0, what does it represent? Is it a number? Is it a set of numbers? Is it shorthand for a limit procedures? It is undefined because, as you have pointed out, any real number will satisfy 0*x = 0, and thus it has ‘infinitely many solution’ - in a crude sense. Then 0/0 cannot represents a single number. Now, should it be a set of numbers? You’ll end up with another problem, divisions most of the times will result in a real number, yet you have a special case where it produces a set. If you want to represent the set of numbers that satisfy 0x = 0, it is much more natural to represent it in set notations: {x in R such that x0 = 0}

yes its undefined, anything divided by 0 is undefined

reddit.com › r/askmath › the function 1 / x when x = 0 becomes undefined but if we had to define to it couldn't we define it as ±∞?

r/askmath on Reddit: The function 1 / x when x = 0 becomes undefined but if we had to define to it couldn't we define it as ±∞?

September 9, 2022 -

In the function 1 / x we see that as x approaches 0 it splits into two values -∞ when x goes from negative to 0 and ∞ when x goes from positive to 0 so why cant we split a value of a function into two different ones? I get that the law of function is to only produce one value but isn't it a bit simplistic for the real world?

±∞ isn't a number. Also, when you approach 0/0 from different ways, the answer is different. For example, as x2/x approaches 0, the limits are ±1. Edit: wrote the limit wrong

Two things. First, functions always produce one value. It's just how they're defined. There are generalizations of functions that produce more than one, but we normally want just one to keep things simple. For instance, imagine we had a "function" g(x) that produces two values: x and -x. Is g(2) equal to 2? 2 = 2, but -2 does not = 2, so neither answer really makes any sense. We want arithmetic statements to have a definite meaning most of the time (which is probably why you feel the need to define 1/0), so this is tough to swallow. Second, even if we treat "±∞" as referring to a single value, we just can't have our familiar division spit it out. Normally, when people talk about some function of "x," they're talking about a function that maps real numbers to other real numbers (or sometimes using complex numbers). ±∞ is neither a real nor complex number. So, in that sense, you can't define it to be ±∞ because, in normal contexts, "±∞" doesn't even exist. There are mathematical systems where you can essentially do what you suggest, like the projectively extended real line , but that's moving to a slightly different system than what we normally use for arithmetic.