A positive or negative number when divided by zero is a fraction with the zero as denominator.
Similar problems occur if one has 0 cookies and 0 people, but this time the problem is in the phrase " the number". A partition is possible of a set with 0 elements into 0 parts , but since the partition has 0 parts, vacuously every set in our partition has a given number of elements, be it 0, 2, 5, or If there are, say, 5 cookies and 2 people, the problem is in "evenly distribute".
In any integer partition of a 5-set into 2 parts, one of the parts of the partition will have more elements than the other. But the problem with 5 cookies and 2 people can be solved by cutting one cookie in half.
The problem with 5 cookies and 0 people cannot be solved in any way that preserves the meaning of "divides". Another way of looking at division by zero is that division can always be checked using multiplication. The Brahmasphutasiddhanta of Brahmagupta — is the earliest known text to treat zero as a number in its own right and to define operations involving zero.
A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator.
Zero divided by zero is zero. In , Mahavira tried unsuccessfully to correct Brahmagupta's mistake in his book in Ganita Sara Samgraha: For instance, to make it possible to subtract any whole number from another, the realm of numbers must be expanded to the entire set of integers in order to incorporate the negative integers. Similarly, to support division of any integer by any other, the realm of numbers must expand to the rational numbers.
During this gradual expansion of the number system, care is taken to ensure that the "extended operations", when applied to the older numbers, do not produce different results.
Loosely speaking, since division by zero has no meaning is undefined in the whole number setting, this remains true as the setting expands to the real or even complex numbers. As the realm of numbers to which these operations can be applied expands there are also changes in how the operations are viewed. For instance, in the realm of integers, subtraction is no longer considered a basic operation since it can be replaced by addition of signed numbers.
In keeping with this change of viewpoint, the question, "Why can't we divide by zero? Answering this revised question precisely requires close examination of the definition of rational numbers. In the modern approach to constructing the field of real numbers, the rational numbers appear as an intermediate step in the development that is founded on set theory.
First, the natural numbers including zero are established on an axiomatic basis such as Peano's axiom system and then this is expanded to the ring of integers.
The next step is to define the rational numbers keeping in mind that this must be done using only the sets and operations that have already been established, namely, addition, multiplication and the integers. This relation is shown to be an equivalence relation and its equivalence classes are then defined to be the rational numbers.
It is in the formal proof that this relation is an equivalence relation that the requirement that the second coordinate is not zero is needed for verifying transitivity.
The above explanation may be too abstract and technical for many purposes, but if one assumes the existence and properties of the rational numbers, as is commonly done in elementary mathematics, the "reason" that division by zero is not allowed is hidden from view.
Nevertheless, a non-rigorous justification can be given in this setting. It follows from the properties of the number system we are using that is, integers, rationals, reals, etc. The concept that explains division in algebra is that it is the inverse of multiplication. In general, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.
A compelling reason for not allowing division by zero is that, if it were allowed, many absurd results i. When working with numerical quantities it is easy to determine when an illegal attempt to divide by zero is being made. For example, consider the following computation.
The fallacy here is the assumption that dividing by 0 is a legitimate operation with the same properties as dividing by any other number. A formal calculation is one carried out using rules of arithmetic, without consideration of whether the result of the calculation is well-defined. I remember being told in school that one of them is undefined and the other is zero but I'm having difficulty with calculating and explaining it to some highly curious 10 year olds! You have twelve cookies to share equally among three children, how many cookies does each child get?
You have eight cookies to share equally among two children, how many cookies does each child get? You have five cookies to share equally among one child, how many cookies does that child get? You have zero cookies to share equally among one child, how many cookies does that child get? You have one cookie to share equally among zero children, how many cookies does each child get?
It is good to 'make sense' out of the choices so that you don't have to rely on memory. How many times can you subtract 0 from 0 before there is nothing left? How about 4 times? However, the left-hand limit is negative infinity. To the best answer. It is NOT infinite. See the theory is if for example lets take 1 divided by 0. It equals infinite right? But then here comes 2. If anyone has any comments please post I am very fascinated by this!!!
This Site Might Help You. Thus acceleration would be infinite mathematically but may be what in terms of physics?????
Please advise how best to explain the distinction between the solution to 'zero divided by one' and 'one divided by zero'. I remember being told in school that one of them is undefined and the other is zero but I'm having difficulty with calculating and explaining it to some highly curious 10 year olds! Why some people say it's 1: A number divided by itself is 1. Why some people say it's undefined: Dividing by zero is undefined. Only one of these explanations is valid, and choosing the other explanations can lead to serious contradictions. If you think of money, which seems to help with fractions, 0/1 is $0 divided evenly among 1 person. We have ALL been there. 1/0 is $1 divided evenly among 0 people, well, if there is no one there,how do we know it is $1. 0/1 is easier to think about, because it is a finite answer, but 1/0 can get tricky.