0 0 undefined why

Learn more. Seeking elegant proof why 0 divided by 0 does not equal 1 Ask Question. Asked 6 years, 11 months ago. Active 2 years, 11 months ago. Viewed 14k times. MJD Doug Kennedy Doug Kennedy 1 1 gold badge 1 1 silver badge 4 4 bronze badges. This is how we know it is impossible to define it in any reasonable way. To say, it's simply undefined so this is invalid is not the way mathematics is done.

OP is interested in why it can't be defined, not in blindly accepting authority. However, saying it's undefined cause it's undefined is a poor argument if it's an argument at all. Add a comment. Active Oldest Votes. Ittay Weiss Ittay Weiss Show 1 more comment.

That is correct, but does not answer OP's question. You did not answer that question. I know why it does not work. We don't get what "a" is because of course, zero times zero does not equal 1. Since it doesn't satisfy at least one part of that definition, then that means that it is considered "undefined.

Well, I think all of us can agree that we can obviously put in a zero there and the second part will be defined. So, this part works. Well, we can also put in a 5 if we wanted to because zero times 5 equals zero, so it still works for that second part. We can actually plug in anything into there.

We can say, zero over zero equals x. We still have zero times x equals zero. But what I'm getting at is that it is the first part that is not being satisfied. Because what happens is that if we can say that zero, 5, or basically any number, then that means that that "c" is not unique. So, in this scenario the first part doesn't work. So, that means that this is going to be undefined.

In this paper [ 1 ], Baron begins the discussion with the following definition:. The powers of any number, are the successive products, arising from unity, continually multiplied, by that number. The first, second, etc. In the same manner, the powers of any number x might be represented as x 1 , x 2 , etc.

After stating a few corollaries, Baron writes:. Let us, therefore, next inquire, whether the same definition, will not lead us to a clear and intelligible solution, of the mysterious paradoxes, resulting from the common definition, when applied, to what is denominated, the nothingth power of numbers. Baron then addresses the rules for dividing powers look back to the argument from the high school text , but he develops a different conclusion:.

But since the number x , is here unlimited with regard to greatness, it follows, that, the nothingth power of an infinite number is equal to a unit. Baron gives credit to both William Emerson [ 3 ] and Jared Mansfield [ 9 ] who wrote on the subject of "nothing. Baron never mentions the term indeterminate form , and he in fact ends his treatise with the following:.

According to Knuth, Libri's paper [ 8 ] "did produce several ripples in mathematical waters when it originally appeared, because it stirred up a controversy about whether 0 0 is defined. Donate Login Sign up Search for courses, skills, and videos. Math Algebra 1 Algebra foundations Division by zero.

Why dividing by zero is undefined. The problem with dividing zero by zero. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript In the last video we saw why when we take any non-zero number divided by zero why mathematicians have left that as being undefined.